Edit Profile (opens in new tab) Poláčik, Peter Co-Author Distance Author ID: polacik.peter Published as: Poláčik, Peter; Poláčik, P.; Polácik, Peter; Polacik, Peter; Poláçik, Peter; Polácik, P. more...less External Links: MGP · Wikidata Videos: carmin.tv Documents Indexed: 112 Publications since 1987, including 2 Books 2 Contributions as Editor Reviewing Activity: 155 Reviews Co-Authors: 40 Co-Authors with 76 Joint Publications 1,251 Co-Co-Authors all top 5 Co-Authors 38 single-authored 10 Yanagida, Eiji 8 Quittner, Pavol 7 Fila, Marek 6 Matano, Hiroshi 6 Valdebenito, Darío A. 5 Brunovský, Pavol 4 Földes, Juraj 4 Húska, Juraj 3 Lou, Yuan 3 Pauthier, Antoine 3 Tereščák, Ignác 2 Chen, Xu-Yan 2 Du, Yihong 2 Fiedler, Bernold 2 Hess, Peter 2 Hutson, Vivian 2 Jendoubi, Mohamed Ali 2 Mischaikow, Konstantin 2 Rybakowski, Krzysztof P. 2 Safonov, Mikhail V. 2 Souplet, Philippe 1 Bartsch, Thomas J. 1 Busca, Jérôme 1 Chen, Chiun-Chuan 1 Dancer, Edward Norman 1 Feireisl, Eduard 1 Haraux, Alain 1 Martínez, Salomé 1 Mierczyński, Janusz 1 Mora, Xavier 1 Ni, Wei-Ming 1 Ninomiya, Hirokazu 1 Peng, Rui 1 Raugel, Geneviève 1 Sandstede, Björn 1 Simondon, Frédérique 1 Solà-Morales, Joan 1 Šošovička, Vladimír 1 Šverák, Vladimír 1 Terracini, Susanna all top 5 Serials 14 Journal of Differential Equations 10 Journal of Dynamics and Differential Equations 8 Discrete and Continuous Dynamical Systems 6 Communications in Partial Differential Equations 5 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 5 SIAM Journal on Mathematical Analysis 3 Archive for Rational Mechanics and Analysis 3 Indiana University Mathematics Journal 3 Journal of Functional Analysis 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Memoirs of the American Mathematical Society 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Differential and Integral Equations 2 Acta Mathematica Universitatis Comenianae. New Series 2 Advances in Differential Equations 2 Discrete and Continuous Dynamical Systems. Series S 2 Nonlinear Analysis. Theory, Methods & Applications 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Biology 1 Nonlinearity 1 Commentationes Mathematicae Universitatis Carolinae 1 Duke Mathematical Journal 1 Mathematische Zeitschrift 1 Transactions of the American Mathematical Society 1 Asymptotic Analysis 1 Mathematica Bohemica 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Tatra Mountains Mathematical Publications 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Evolution Equations 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Fixed Point Theory and Applications 1 Networks and Heterogeneous Media 1 São Paulo Journal of Mathematical Sciences 1 SN Partial Differential Equations and Applications all top 5 Fields 109 Partial differential equations (35-XX) 18 Dynamical systems and ergodic theory (37-XX) 9 Global analysis, analysis on manifolds (58-XX) 4 Ordinary differential equations (34-XX) 4 Biology and other natural sciences (92-XX) 3 Operator theory (47-XX) 2 General and overarching topics; collections (00-XX) 2 Algebraic topology (55-XX) 1 History and biography (01-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 105 Publications have been cited 2,011 times in 1,141 Documents Cited by ▼ Year ▼ Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038 Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 259 2007 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035 Hutson, V.; Mischaikow, K.; Poláčik, P. 111 2001 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051 Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 92 2007 On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055 Poláčik, Peter; Yanagida, Eiji 74 2003 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039 Poláčik, P.; Tereščák, I. 58 1991 Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002 Poláčik, P.; Tereščák, Ignác 53 1993 Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059 Chen, Xu-Yan; Poláčik, Peter 49 1996 Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064 Poláčik, Peter 49 1989 Competing species near a degenerate limit. Zbl 1043.35080 Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 40 2003 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001 Poláčik, P. 39 2002 On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098 Földes, J.; Poláčik, Peter 38 2009 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060 Fiedler, Bernold; Poláčik, Peter 35 1990 Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011 Lou, Yuan; Martínez, Salomé; Poláčik, Peter 33 2006 Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002 Poláčik, Peter 33 2020 Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013 Busca, J.; Jendoubi, M. A.; Poláčik, P. 32 2002 Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054 Poláčik, Peter; Rybakowski, Krzysztof P. 32 1996 The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062 Brunovský, P.; Poláčik, P. 32 1997 Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130 Poláčik, P. 32 2011 Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009 Brunovský, P.; Poláčik, P.; Sandstede, B. 31 1992 Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207 Du, Yihong; Poláčik, Peter 30 2015 A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045 Poláčik, Peter; Quittner, Pavol 30 2006 Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041 Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol 28 2011 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052 Matano, H.; Poláčik, P. 28 2016 Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049 Hess, Peter; Poláčik, P. 26 1994 A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044 Poláčik, P.; Yanagida, E. 26 2005 Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046 Poláčik, P.; Simondon, F. 24 2002 Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079 Feireisl, Eduard; Poláčik, Peter 23 2000 Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011 Haraux, A.; Poláčik, P. 22 1992 Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046 Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. 21 2007 Monotonicity of stable solutions in shadow systems. Zbl 0981.35018 Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji 20 2001 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045 Poláčik, P. 20 2005 Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008 Poláčik, P.; Tereščák, I. 19 1994 Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027 Poláčik, Peter 19 1991 Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077 Hess, Peter; Poláčik, Peter 18 1993 Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 1516.35089 Poláčik, P. 18 2017 Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097 Poláčik, P. 17 2015 Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063 Poláčik, Peter 17 2007 Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035 Földes, Juraj; Poláčik, P. 17 2011 Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037 Poláčik, Peter; Quittner, Pavol 17 2005 Immediate regularization after blow-up. Zbl 1102.35053 Fila, Marek; Matano, Hiroshi; Polácik, Peter 17 2005 Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039 Poláčik, P. 16 2016 Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045 Jendoubi, M. A.; Poláčik, P. 15 2003 On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048 Brunovský, P.; Poláčik, P. 14 1997 Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153 Poláčik, P.; Šverák, V. 14 2008 Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073 Chen, Xu-Yan; Poláčik, Peter 13 1995 High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060 Poláčik, Peter 13 1995 Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042 Poláčik, P. 13 2009 Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016 Poláčik, Peter; Valdebenito, Darío A. 13 2017 Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148 Poláčik, Peter; Yanagida, Eiji 13 2014 The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353 Húska, Juraj; Poláčik, Peter 12 2004 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051 Poláčik, P. 12 2006 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200 Matano, H.; Poláčik, P. 12 2020 Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060 Dancer, E. N.; Poláčik, P. 11 1999 Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321 Poláčik, Peter 10 2001 Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041 Poláčik, Peter 10 1991 Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130 Poláčik, Peter 9 2015 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076 Pauthier, Antoine; Poláčik, Peter 9 2018 On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030 Poláčik, P. 8 2005 Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046 Poláčik, P. 8 1992 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030 Fila, Marek; Poláčik, Peter 8 1999 Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403 Poláčik, P.; Yanagida, E. 8 2004 The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127 Du, Yihong; Peng, Rui; Poláçik, Peter 8 2012 An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152 Matano, H.; Poláčik, P. 8 2017 Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036 Poláčik, Peter 7 1989 Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043 Poláčik, P. 7 1990 Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041 Poláčik, Peter 6 1994 Global solutions of a semilinear parabolic equation. Zbl 0953.35065 Fila, Marek; Poláčik, Peter 6 1999 Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021 Húska, Juraj; Poláčik, Peter 6 2008 Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304 Poláčik, P. 6 2020 Group actions on strongly monotone dynamical systems. Zbl 0642.58031 Mierczyński, Janusz; Poláčik, Peter 6 1989 Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039 Poláčik, Peter 6 1987 Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228 Poláčik, Peter; Quittner, Pavol 6 2021 Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009 Poláčik, P. 5 2002 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054 Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074 Poláčik, Peter; Rybakowski, Krzysztof 5 1995 Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065 Poláčik, Peter; Šošovička, Vladimír 5 1996 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056 Pauthier, Antoine; Poláčik, Peter 5 2021 Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083 Poláčik, P. 5 2011 On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073 Poláčik, P. 5 2012 Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109 Poláčik, P.; Terracini, Susanna 5 2014 Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150 Poláčik, Peter; Yanagida, Eiji 5 2009 Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013 Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J. 4 1991 Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023 Poláčik, Peter; Yanagida, Eiji 4 2001 Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093 Poláčik, P. 4 2017 Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391 Húska, J.; Poláčik, P.; Safonov, M. V. 4 2005 Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026 Poláčik, Peter; Valdebenito, Darío A. 4 2020 Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005 Brunovský, Pavol; Poláčik, Peter 4 1987 Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109 Poláčik, Peter; Yanagida, Eiji 4 2014 On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034 Poláčik, Peter 4 2014 Immediate regularization after blow-up. Zbl 1108.35092 Fila, M.; Matano, H.; Poláčik, P. 3 2005 Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014 Poláčik, Peter; Quittner, Pavol 3 2008 Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on \(\mathbb{R}^{N+1}\). Zbl 1479.35412 Poláčik, Peter; Valdebenito, Darío A. 3 2020 Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051 Poláčik, Peter; Yanagida, Eiji 2 2002 Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065 Poláčik, Peter 2 1994 Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097 Poláčik, Peter 2 1999 On asymptotically symmetric parabolic equations. Zbl 1262.35041 Földes, Juraj; Poláčik, Peter 2 2012 Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054 Poláčik, Peter 2 1990 On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170 Poláčik, P.; Quittner, P. 2 2020 Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074 Poláčik, P. 2 2012 Equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains. Zbl 1328.35109 Földes, J.; Poláčik, P. 2 2015 On bounded radial solutions of parabolic equations on \(\mathbb{R}^N \): quasiconvergence for initial data with a stable limit at infinity. Zbl 1542.35216 Poláčik, Peter 1 2024 Nonexistence of radial time-periodic solutions of reaction-diffusion equations with generic nonlinearities. Zbl 1514.35268 Poláčik, Peter 1 2023 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. III: Unstable limit at infinity. Zbl 1495.35039 Pauthier, Antoine; Poláčik, Peter 2 2022 The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space. (https://www.zentralblatt-math.org/math/correction/.) Zbl 1501.35148 Poláčik, Peter; Valdebenito, Darío A. 1 2022 Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228 Poláčik, Peter; Quittner, Pavol 6 2021 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056 Pauthier, Antoine; Poláčik, Peter 5 2021 Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002 Poláčik, Peter 33 2020 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200 Matano, H.; Poláčik, P. 12 2020 Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304 Poláčik, P. 6 2020 Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026 Poláčik, Peter; Valdebenito, Darío A. 4 2020 Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on \(\mathbb{R}^{N+1}\). Zbl 1479.35412 Poláčik, Peter; Valdebenito, Darío A. 3 2020 On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170 Poláčik, P.; Quittner, P. 2 2020 Some generic properties of Schrödinger operators with radial potentials. Zbl 1436.35099 Poláčik, Peter; Valdebenito, Darío A. 1 2019 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076 Pauthier, Antoine; Poláčik, Peter 9 2018 Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 1516.35089 Poláčik, P. 18 2017 Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016 Poláčik, Peter; Valdebenito, Darío A. 13 2017 An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152 Matano, H.; Poláčik, P. 8 2017 Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093 Poláčik, P. 4 2017 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences. Zbl 1345.35052 Matano, H.; Poláčik, P. 28 2016 Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039 Poláčik, P. 16 2016 Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207 Du, Yihong; Poláčik, Peter 30 2015 Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097 Poláčik, P. 17 2015 Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130 Poláčik, Peter 9 2015 Equilibria with a nontrivial nodal set and the dynamics of parabolic equations on symmetric domains. Zbl 1328.35109 Földes, J.; Poláčik, P. 2 2015 Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148 Poláčik, Peter; Yanagida, Eiji 13 2014 Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109 Poláčik, P.; Terracini, Susanna 5 2014 Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109 Poláčik, Peter; Yanagida, Eiji 4 2014 On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034 Poláčik, Peter 4 2014 The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127 Du, Yihong; Peng, Rui; Poláçik, Peter 8 2012 On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073 Poláčik, P. 5 2012 On asymptotically symmetric parabolic equations. Zbl 1262.35041 Földes, Juraj; Poláčik, Peter 2 2012 Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074 Poláčik, P. 2 2012 Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130 Poláčik, P. 32 2011 Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041 Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol 28 2011 Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035 Földes, Juraj; Poláčik, P. 17 2011 Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083 Poláčik, P. 5 2011 On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098 Földes, J.; Poláčik, Peter 38 2009 Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042 Poláčik, P. 13 2009 Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150 Poláčik, Peter; Yanagida, Eiji 5 2009 Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153 Poláčik, P.; Šverák, V. 14 2008 Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021 Húska, Juraj; Poláčik, Peter 6 2008 Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014 Poláčik, Peter; Quittner, Pavol 3 2008 Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038 Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 259 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051 Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 92 2007 Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046 Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. 21 2007 Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063 Poláčik, Peter 17 2007 Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011 Lou, Yuan; Martínez, Salomé; Poláčik, Peter 33 2006 A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045 Poláčik, Peter; Quittner, Pavol 30 2006 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051 Poláčik, P. 12 2006 A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044 Poláčik, P.; Yanagida, E. 26 2005 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045 Poláčik, P. 20 2005 Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037 Poláčik, Peter; Quittner, Pavol 17 2005 Immediate regularization after blow-up. Zbl 1102.35053 Fila, Marek; Matano, Hiroshi; Polácik, Peter 17 2005 On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030 Poláčik, P. 8 2005 Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391 Húska, J.; Poláčik, P.; Safonov, M. V. 4 2005 Immediate regularization after blow-up. Zbl 1108.35092 Fila, M.; Matano, H.; Poláčik, P. 3 2005 The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353 Húska, Juraj; Poláčik, Peter 12 2004 Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403 Poláčik, P.; Yanagida, E. 8 2004 On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055 Poláčik, Peter; Yanagida, Eiji 74 2003 Competing species near a degenerate limit. Zbl 1043.35080 Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 40 2003 Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045 Jendoubi, M. A.; Poláčik, P. 15 2003 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001 Poláčik, P. 39 2002 Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013 Busca, J.; Jendoubi, M. A.; Poláčik, P. 32 2002 Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046 Poláčik, P.; Simondon, F. 24 2002 Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009 Poláčik, P. 5 2002 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054 Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051 Poláčik, Peter; Yanagida, Eiji 2 2002 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035 Hutson, V.; Mischaikow, K.; Poláčik, P. 111 2001 Monotonicity of stable solutions in shadow systems. Zbl 0981.35018 Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji 20 2001 Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321 Poláčik, Peter 10 2001 Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023 Poláčik, Peter; Yanagida, Eiji 4 2001 Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079 Feireisl, Eduard; Poláčik, Peter 23 2000 Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060 Dancer, E. N.; Poláčik, P. 11 1999 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030 Fila, Marek; Poláčik, Peter 8 1999 Global solutions of a semilinear parabolic equation. Zbl 0953.35065 Fila, Marek; Poláčik, Peter 6 1999 Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097 Poláčik, Peter 2 1999 The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062 Brunovský, P.; Poláčik, P. 32 1997 On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048 Brunovský, P.; Poláčik, P. 14 1997 Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059 Chen, Xu-Yan; Poláčik, Peter 49 1996 Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054 Poláčik, Peter; Rybakowski, Krzysztof P. 32 1996 Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065 Poláčik, Peter; Šošovička, Vladimír 5 1996 Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073 Chen, Xu-Yan; Poláčik, Peter 13 1995 High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060 Poláčik, Peter 13 1995 Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074 Poláčik, Peter; Rybakowski, Krzysztof 5 1995 Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049 Hess, Peter; Poláčik, P. 26 1994 Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008 Poláčik, P.; Tereščák, I. 19 1994 Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041 Poláčik, Peter 6 1994 Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065 Poláčik, Peter 2 1994 Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002 Poláčik, P.; Tereščák, Ignác 53 1993 Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077 Hess, Peter; Poláčik, Peter 18 1993 Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009 Brunovský, P.; Poláčik, P.; Sandstede, B. 31 1992 Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011 Haraux, A.; Poláčik, P. 22 1992 Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046 Poláčik, P. 8 1992 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039 Poláčik, P.; Tereščák, I. 58 1991 Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027 Poláčik, Peter 19 1991 Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041 Poláčik, Peter 10 1991 Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013 Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J. 4 1991 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060 Fiedler, Bernold; Poláčik, Peter 35 1990 Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043 Poláčik, P. 7 1990 Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054 Poláčik, Peter 2 1990 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,111 Authors 58 Poláčik, Peter 35 Lou, Yuan 22 Shen, Wenxian 21 Wang, Yi 18 Yanagida, Eiji 17 Wei, Juncheng 16 Winkler, Michael 15 Souplet, Philippe 14 Mizoguchi, Noriko 14 Peng, Rui 14 Wang, Zhicheng 13 Fila, Marek 13 Lam, King-Yeung 13 Obaya, Rafael 13 Quittner, Pavol 12 Matano, Hiroshi 12 Weth, Tobias 11 Du, Yihong 11 Jendoubi, Mohamed Ali 11 Lou, Bendong 11 Mierczyński, Janusz 11 Phan, Quoc Hung 11 Vakulenko, Sergei A. 10 Duong, Anh Tuan 10 Hamel, François 10 Ishige, Kazuhiro 10 Jiang, Jifa 10 Li, Wan-Tong 10 Zhao, Xiao-Qiang 9 Dai, Wei 9 Guo, Zongming 9 Liu, Shuang 9 Sanz, Ana M. 9 Villavert, John 9 Zhou, Maolin 9 Zou, Wenming 8 Cantrell, Robert Stephen 8 Cosner, Chris 8 Giletti, Thomas 8 Peng, Shaolong 8 Yi, Taishan 8 Zhang, Zhengce 8 Zhang, Zhitao 7 Bo, Wei-Jian 7 Chill, Ralph 7 Ding, Weiwei 7 Földes, Juraj 7 Harrabi, Abdellaziz 7 Langa, Jose’ Antonio 7 Lin, Guo 7 Qin, Guolin 7 Ruan, Shigui 7 Shi, Junping 7 Smith, Hal Leslie 7 Valdebenito, Darío A. 7 Vishnevskii, Mikhail P. 7 Wang, Yuxia 6 Alfaro, Matthieu 6 Bao, Jiguang 6 Dancer, Edward Norman 6 Kawakami, Tatsuki 6 Li, Yimei 6 Nadin, Grégoire 6 Wu, Jianhua 6 Yang, Hui 6 Yao, Jinxiang 6 Zhou, Dun 5 Berestycki, Henri 5 Chen, Wenxiong 5 Ducrot, Arnaud 5 Fiedler, Bernold 5 García-Melián, Jorge 5 Giga, Yoshikazu 5 Girardin, Léo 5 Hoshino, Masaki 5 Huang, Haochuan 5 Huang, Rui 5 Jänig, Axel 5 Joly, Romain 5 Li, Congming 5 Li, Kui 5 Miyamoto, Yasuhito 5 Mtiri, Foued 5 Nolasco de Carvalho, Alexandre 5 Pierre, Morgan 5 Raugel, Geneviève 5 Rocha, Carlos 5 Rodríguez-Bernal, Aníbal 5 Roquejoffre, Jean-Michel 5 Saldaña, Alberto 5 Vazquez, Juan Luis 5 Vétois, Jérôme 5 Wan, FangShu 5 Wang, Mingxin 5 Wu, Hao 5 Wu, Leyun 5 Zhang, Liang 5 Zhang, Rong 4 Bidaut-Veron, Marie-Françoise 4 Brunovský, Pavol ...and 1,011 more Authors all top 5 Cited in 192 Serials 160 Journal of Differential Equations 61 Journal of Dynamics and Differential Equations 60 Journal of Mathematical Analysis and Applications 48 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 37 Calculus of Variations and Partial Differential Equations 35 Discrete and Continuous Dynamical Systems 29 Communications on Pure and Applied Analysis 23 Journal of Functional Analysis 22 Nonlinear Analysis. Real World Applications 22 Discrete and Continuous Dynamical Systems. Series B 20 Journal of Mathematical Biology 19 Transactions of the American Mathematical Society 19 Journal de Mathématiques Pures et Appliquées. Neuvième Série 18 SIAM Journal on Mathematical Analysis 17 Nonlinearity 17 Mathematische Annalen 16 Proceedings of the American Mathematical Society 16 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 14 Communications in Contemporary Mathematics 13 Advances in Mathematics 13 NoDEA. Nonlinear Differential Equations and Applications 12 Communications in Partial Differential Equations 11 Archive for Rational Mechanics and Analysis 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Journal of Evolution Equations 11 Discrete and Continuous Dynamical Systems. Series S 9 Science China. Mathematics 8 Journal d’Analyse Mathématique 8 Bulletin of Mathematical Biology 8 Advances in Nonlinear Analysis 7 Mathematische Nachrichten 7 Applied Mathematics Letters 7 Advances in Difference Equations 7 Complex Variables and Elliptic Equations 6 Applicable Analysis 6 Siberian Mathematical Journal 6 Journal of Biological Dynamics 6 Journal of Fixed Point Theory and Applications 5 Mathematical Methods in the Applied Sciences 5 Memoirs of the American Mathematical Society 5 Acta Applicandae Mathematicae 5 Journal of Difference Equations and Applications 5 Advanced Nonlinear Studies 4 Mathematical Biosciences 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Mathematische Zeitschrift 4 SIAM Journal on Applied Mathematics 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Journal of Nonlinear Science 4 Electronic Journal of Differential Equations (EJDE) 4 Revista Matemática Complutense 4 Milan Journal of Mathematics 4 Mathematical Biosciences and Engineering 4 Boundary Value Problems 4 Journal of Elliptic and Parabolic Equations 4 SN Partial Differential Equations and Applications 3 Communications in Mathematical Physics 3 Communications on Pure and Applied Mathematics 3 Rocky Mountain Journal of Mathematics 3 Chaos, Solitons and Fractals 3 Archiv der Mathematik 3 Journal of Computational and Applied Mathematics 3 Journal of the London Mathematical Society. Second Series 3 Quarterly of Applied Mathematics 3 Zeitschrift für Analysis und ihre Anwendungen 3 Physica D 3 Topological Methods in Nonlinear Analysis 3 Journal of the European Mathematical Society (JEMS) 3 Acta Mathematica Sinica. English Series 3 Communications in Nonlinear Science and Numerical Simulation 3 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Journal of Applied Analysis and Computation 3 AIMS Mathematics 3 Mathematics in Engineering 2 Bulletin of the Australian Mathematical Society 2 Computers & Mathematics with Applications 2 Journal of Mathematical Physics 2 Mathematical Notes 2 Journal of Geometry and Physics 2 Acta Mathematica 2 Collectanea Mathematica 2 Indiana University Mathematics Journal 2 Journal of the Korean Mathematical Society 2 Manuscripta Mathematica 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Tôhoku Mathematical Journal. Second Series 2 Chinese Annals of Mathematics. Series B 2 Acta Mathematicae Applicatae Sinica. English Series 2 Numerical Methods for Partial Differential Equations 2 Journal of Integral Equations and Applications 2 International Journal of Mathematics 2 The Journal of Geometric Analysis 2 Bulletin des Sciences Mathématiques 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Taiwanese Journal of Mathematics ...and 92 more Serials all top 5 Cited in 36 Fields 995 Partial differential equations (35-XX) 221 Biology and other natural sciences (92-XX) 168 Dynamical systems and ergodic theory (37-XX) 88 Ordinary differential equations (34-XX) 41 Operator theory (47-XX) 32 Integral equations (45-XX) 26 Global analysis, analysis on manifolds (58-XX) 22 Fluid mechanics (76-XX) 18 Numerical analysis (65-XX) 15 Differential geometry (53-XX) 12 Systems theory; control (93-XX) 11 Difference and functional equations (39-XX) 11 Probability theory and stochastic processes (60-XX) 10 Functional analysis (46-XX) 8 Potential theory (31-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Real functions (26-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 General topology (54-XX) 6 Mechanics of particles and systems (70-XX) 6 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Functions of a complex variable (30-XX) 3 Quantum theory (81-XX) 2 Combinatorics (05-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 1 General and overarching topics; collections (00-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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