Edit Profile (opens in new tab) Poláčik, Peter Compute Distance To: Compute Author ID: polacik.peter Published as: Poláčik, Peter; Poláčik, P.; Polácik, Peter; Polacik, Peter; Poláçik, Peter; Polácik, P. more...less External Links: MGP Documents Indexed: 110 Publications since 1987, including 2 Books 1 Contribution as Editor Reviewing Activity: 155 Reviews Co-Authors: 39 Co-Authors with 73 Joint Publications 1,169 Co-Co-Authors all top 5 Co-Authors 36 single-authored 10 Yanagida, Eiji 8 Quittner, Pavol 6 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 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 Fiedler, Bernold 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 9 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 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 Discrete and Continuous Dynamical Systems. Series S 1 SN Partial Differential Equations and Applications all top 5 Fields 107 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 Algebraic topology (55-XX) 1 General and overarching topics; collections (00-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 101 Publications have been cited 1,648 times in 938 Documents Cited by ▼ Year ▼ Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 200 2007 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035Hutson, V.; Mischaikow, K.; Poláčik, P. 95 2001 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 71 2007 On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055Poláčik, Peter; Yanagida, Eiji 66 2003 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039Poláčik, P.; Tereščák, I. 51 1991 Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002Poláčik, P.; Tereščák, Ignác 49 1993 Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064Poláčik, Peter 42 1989 Competing species near a degenerate limit. Zbl 1043.35080Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 39 2003 Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059Chen, Xu-Yan; Poláčik, Peter 37 1996 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001Poláčik, P. 34 2002 Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054Poláčik, Peter; Rybakowski, Krzysztof P. 32 1996 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060Fiedler, Bernold; Poláčik, Peter 32 1990 The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062Brunovský, P.; Poláčik, P. 30 1997 Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009Brunovský, P.; Poláčik, P.; Sandstede, B. 29 1992 On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098Földes, J.; Poláčik, Peter 29 2009 Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011Lou, Yuan; Martínez, Salomé; Poláčik, Peter 28 2006 Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013Busca, J.; Jendoubi, M. A.; Poláčik, P. 26 2002 Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol 25 2011 A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045Poláčik, Peter; Quittner, Pavol 25 2006 Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130Poláčik, P. 25 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 1345.35052Matano, H.; Poláčik, P. 22 2016 A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044Poláčik, P.; Yanagida, E. 22 2005 Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046Poláčik, P.; Simondon, F. 22 2002 Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207Du, Yihong; Poláčik, Peter 21 2015 Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049Hess, Peter; Poláčik, P. 21 1994 Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079Feireisl, Eduard; Poláčik, Peter 21 2000 Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011Haraux, A.; Poláčik, P. 20 1992 Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. 19 2007 Monotonicity of stable solutions in shadow systems. Zbl 0981.35018Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji 19 2001 Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027Poláčik, Peter 18 1991 Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077Hess, Peter; Poláčik, Peter 17 1993 Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008Poláčik, P.; Tereščák, I. 17 1994 Immediate regularization after blow-up. Zbl 1102.35053Fila, Marek; Matano, Hiroshi; Polácik, Peter 16 2005 Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002Poláčik, Peter 14 2020 Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097Poláčik, P. 13 2015 On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048Brunovský, P.; Poláčik, P. 12 1997 Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063Poláčik, Peter 12 2007 Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039Poláčik, P. 12 2016 High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060Poláčik, Peter 12 1995 Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016Poláčik, Peter; Valdebenito, Darío A. 12 2017 Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 06780933Poláčik, P. 12 2017 Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060Dancer, E. N.; Poláčik, P. 11 1999 Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073Chen, Xu-Yan; Poláčik, Peter 11 1995 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045Poláčik, P. 11 2005 Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042Poláčik, P. 11 2009 Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035Földes, Juraj; Poláčik, P. 11 2011 Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321Poláčik, Peter 10 2001 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051Poláčik, P. 10 2006 The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353Húska, Juraj; Poláčik, Peter 10 2004 Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153Poláčik, P.; Šverák, V. 9 2008 Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045Jendoubi, M. A.; Poláčik, P. 9 2003 Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041Poláčik, Peter 9 1991 Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037Poláčik, Peter; Quittner, Pavol 9 2005 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030Fila, Marek; Poláčik, Peter 8 1999 Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403Poláčik, P.; Yanagida, E. 8 2004 On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030Poláčik, P. 8 2005 Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046Poláčik, P. 8 1992 An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152Matano, H.; Poláčik, P. 8 2017 Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148Poláčik, Peter; Yanagida, Eiji 8 2014 Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036Poláčik, Peter 7 1989 The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127Du, Yihong; Peng, Rui; Poláçik, Peter 7 2012 Global solutions of a semilinear parabolic equation. Zbl 0953.35065Fila, Marek; Poláčik, Peter 6 1999 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200Matano, H.; Poláčik, P. 6 2020 Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041Poláčik, Peter 6 1994 Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039Poláčik, Peter 6 1987 Group actions on strongly monotone dynamical systems. Zbl 0642.58031Mierczyński, Janusz; Poláčik, Peter 6 1989 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076Pauthier, Antoine; Poláčik, Peter 5 2018 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009Poláčik, P. 5 2002 Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074Poláčik, Peter; Rybakowski, Krzysztof 5 1995 Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109Poláčik, P.; Terracini, Susanna 5 2014 On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073Poláčik, P. 5 2012 Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083Poláčik, P. 5 2011 Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130Poláčik, Peter 5 2015 Generic hyperbolicity for reaction diffusion equations on symmetric domains. Zbl 0622.35005Brunovský, Pavol; Poláčik, Peter 4 1987 Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021Húska, Juraj; Poláčik, Peter 4 2008 Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304Poláčik, P. 4 2020 Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228Poláčik, Peter; Quittner, Pavol 4 2021 Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065Poláčik, Peter; Šošovička, Vladimír 4 1996 Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J. 4 1991 Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150Poláčik, Peter; Yanagida, Eiji 4 2009 On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034Poláčik, Peter 4 2014 Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026Poláčik, Peter; Valdebenito, Darío A. 4 2020 Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109Poláčik, Peter; Yanagida, Eiji 4 2014 Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014Poláčik, Peter; Quittner, Pavol 3 2008 Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391Húska, J.; Poláčik, P.; Safonov, M. V. 3 2005 Immediate regularization after blow-up. Zbl 1108.35092Fila, M.; Matano, H.; Poláčik, P. 3 2005 Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023Poláčik, Peter; Yanagida, Eiji 3 2001 Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093Poláčik, P. 3 2017 Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065Poláčik, Peter 2 1994 Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051Poláčik, Peter; Yanagida, Eiji 2 2002 On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170Poláčik, P.; Quittner, P. 2 2020 Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097Poláčik, Peter 2 1999 Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043Poláčik, P. 2 1990 Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054Poláčik, Peter 2 1990 Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074Poláčik, P. 2 2012 Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on \(\mathbb{R}^{N+1}\). Zbl 1479.35412Poláčik, Peter; Valdebenito, Darío A. 2 2020 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056Pauthier, Antoine; Poláčik, Peter 2 2021 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 1501.35148Poláčik, Peter; Valdebenito, Darío A. 1 2022 Some generic properties of Schrödinger operators with radial potentials. Zbl 1436.35099Poláčik, Peter; Valdebenito, Darío A. 1 2019 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 1501.35148Poláčik, Peter; Valdebenito, Darío A. 1 2022 Entire and ancient solutions of a supercritical semilinear heat equation. Zbl 1458.35228Poláčik, Peter; Quittner, Pavol 4 2021 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. II: Equal limits at infinity. Zbl 1473.35056Pauthier, Antoine; Poláčik, Peter 2 2021 Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on \(\mathbb{R}\). Zbl 1450.35002Poláčik, Peter 14 2020 Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. II: Generic nonlinearities. Zbl 1439.35200Matano, H.; Poláčik, P. 6 2020 Entire solutions and a Liouville theorem for a class of parabolic equations on the real line. Zbl 1448.35304Poláčik, P. 4 2020 Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity. Zbl 1439.35026Poláčik, Peter; Valdebenito, Darío A. 4 2020 On the multiplicity of self-similar solutions of the semilinear heat equation. Zbl 1428.35170Poláčik, P.; Quittner, P. 2 2020 Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on \(\mathbb{R}^{N+1}\). Zbl 1479.35412Poláčik, Peter; Valdebenito, Darío A. 2 2020 Some generic properties of Schrödinger operators with radial potentials. Zbl 1436.35099Poláčik, Peter; Valdebenito, Darío A. 1 2019 Large-time behavior of solutions of parabolic equations on the real line with convergent initial data. Zbl 1393.35076Pauthier, Antoine; Poláčik, Peter 5 2018 Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems. Zbl 1372.35016Poláčik, Peter; Valdebenito, Darío A. 12 2017 Planar propagating terraces and the asymptotic one-dimensional symmetry of solutions of semilinear parabolic equations. Zbl 06780933Poláčik, P. 12 2017 An entire solution of a bistable parabolic equation on \(\mathbb{R}\) with two colliding pulses. Zbl 1362.35152Matano, H.; Poláčik, P. 8 2017 Propagating terraces in a proof of the Gibbons conjecture and related results. Zbl 1366.35093Poláčik, P. 3 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 1345.35052Matano, H.; Poláčik, P. 22 2016 Threshold behavior and non-quasiconvergent solutions with localized initial data for bistable reaction-diffusion equations. Zbl 1456.35039Poláčik, P. 12 2016 Locally uniform convergence to an equilibrium for nonlinear parabolic equations on \(\mathbb{R}^N\). Zbl 1336.35207Du, Yihong; Poláčik, Peter 21 2015 Examples of bounded solutions with nonstationary limit profiles for semilinear heat equations on \({\mathbb{R}}\). Zbl 1319.35097Poláčik, P. 13 2015 Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations. Zbl 1334.35130Poláčik, Peter 5 2015 Localized solutions of a semilinear parabolic equation with a recurrent nonstationary asymptotics. Zbl 1316.35148Poláčik, Peter; Yanagida, Eiji 8 2014 Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains. Zbl 1286.35109Poláčik, P.; Terracini, Susanna 5 2014 On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Zbl 1285.35034Poláčik, Peter 4 2014 Global unbounded solutions of the Fujita equation in the intermediate range. Zbl 1319.35109Poláčik, Peter; Yanagida, Eiji 4 2014 The parabolic logistic equation with blow-up initial and boundary values. Zbl 1308.35127Du, Yihong; Peng, Rui; Poláçik, Peter 7 2012 On symmetry of nonnegative solutions of elliptic equations. Zbl 1241.35073Poláčik, P. 5 2012 Positivity and symmetry of nonnegative solutions of semilinear elliptic equations on planar domains. Zbl 1243.35074Poláčik, P. 2 2012 On asymptotically symmetric parabolic equations. Zbl 1262.35041Földes, Juraj; Poláčik, Peter 1 2012 Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Zbl 1215.35041Bartsch, Thomas; Poláčik, Peter; Quittner, Pavol 25 2011 Threshold solutions and sharp transitions for nonautonomous parabolic equations on \({\mathbb{R}^N}\). Zbl 1262.35130Poláčik, P. 25 2011 Convergence to a steady state for asymptotically autonomous semilinear heat equations on \(\mathbb R^N\). Zbl 1263.35035Földes, Juraj; Poláčik, P. 11 2011 Symmetry of nonnegative solutions of elliptic equations via a result of Serrin. Zbl 1241.35083Poláčik, P. 5 2011 On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Zbl 1178.35098Földes, J.; Poláčik, Peter 29 2009 Symmetry properties of positive solutions of parabolic equations: a survey. Zbl 1213.35042Poláčik, P. 11 2009 Convergence of anisotropically decaying solutions of a supercritical semilinear heat equation. Zbl 1197.35150Poláčik, Peter; Yanagida, Eiji 4 2009 Zeros of complex caloric functions and singularities of complex viscous Burgers equation. Zbl 1188.35153Poláčik, P.; Šverák, V. 9 2008 Exponential separation and principal Floquet bundles for linear parabolic equations on \(\mathbb R^N\). Zbl 1170.35021Húska, Juraj; Poláčik, Peter 4 2008 Asymptotic behavior of threshold and sub-threshold solutions of a semilinear heat equation. Zbl 1153.35014Poláčik, Peter; Quittner, Pavol 3 2008 Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems. Zbl 1146.35038Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 200 2007 Singularity and decay estimates in superlinear problems via Liouville-type theorems. II: Parabolic equations. Zbl 1122.35051Poláčik, Peter; Quittner, Pavol; Souplet, Philippe 71 2007 Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Zbl 1139.35046Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. 19 2007 Estimates of solutions and asymptotic symmetry for parabolic equations on bounded domains. Zbl 1171.35063Poláčik, Peter 12 2007 Loops and branches of coexistence states in a Lotka–Volterra competition model. Zbl 1154.35011Lou, Yuan; Martínez, Salomé; Poláčik, Peter 28 2006 A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation. Zbl 1092.35045Poláčik, Peter; Quittner, Pavol 25 2006 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). II: Entire solutions. Zbl 1128.35051Poláčik, P. 10 2006 A Liouville property and quasiconvergence for a semilinear heat equation. Zbl 1068.35044Poláčik, P.; Yanagida, E. 22 2005 Immediate regularization after blow-up. Zbl 1102.35053Fila, Marek; Matano, Hiroshi; Polácik, Peter 16 2005 Symmetry properties of positive solutions of parabolic equations on \(\mathbb R^N\). I: Asymptotic symmetry for the Cauchy problem. Zbl 1083.35045Poláčik, P. 11 2005 Liouville type theorems and complete blow-up for indefinite superlinear parabolic equations. Zbl 1093.35037Poláčik, Peter; Quittner, Pavol 9 2005 On uniqueness of positive entire solutions and other properties of linear parabolic equations. Zbl 1067.35030Poláčik, P. 8 2005 Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Zbl 1152.35391Húska, J.; Poláčik, P.; Safonov, M. V. 3 2005 Immediate regularization after blow-up. Zbl 1108.35092Fila, M.; Matano, H.; Poláčik, P. 3 2005 The principal Floquet bundle and exponential separation for linear parabolic equations. Zbl 1128.35353Húska, Juraj; Poláčik, Peter 10 2004 Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Zbl 1174.35403Poláčik, P.; Yanagida, E. 8 2004 On bounded and unbounded global solutions of a supercritical semilinear heat equation. Zbl 1055.35055Poláčik, Peter; Yanagida, Eiji 66 2003 Competing species near a degenerate limit. Zbl 1043.35080Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 39 2003 Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping. Zbl 1046.37045Jendoubi, M. A.; Poláčik, P. 9 2003 Parabolic equations: Asymptotic behavior and dynamics on invariant manifolds. Zbl 1002.35001Poláčik, P. 34 2002 Convergence to equilibrium for semilinear parabolic problems in \(\mathbb{R}^N\). Zbl 1021.35013Busca, J.; Jendoubi, M. A.; Poláčik, P. 26 2002 Nonconvergent bounded solutions of semilinear heat equations on arbitrary domains. Zbl 1024.35046Poláčik, P.; Simondon, F. 22 2002 Existence of \(L^1\)-connections between equilibria of a semilinear parabolic equation. Zbl 1001.35054Fila, Marek; Matano, Hiroshi; Poláčik, Peter 5 2002 Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations. Zbl 1010.35009Poláčik, P. 5 2002 Stable subharmonic solutions of reaction-diffusion equations on an arbitrary domain. Zbl 0993.35051Poláčik, Peter; Yanagida, Eiji 2 2002 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035Hutson, V.; Mischaikow, K.; Poláčik, P. 95 2001 Monotonicity of stable solutions in shadow systems. Zbl 0981.35018Ni, Wei-Ming; Polácik, Peter; Yanagida, Eiji 19 2001 Morse indices and bifurcations of positive solutions of \(\Delta u+f(u)=0\) on \(\mathbb R^ N\). Zbl 1101.35321Poláčik, Peter 10 2001 Existence of stable subharmonic solutions for reaction-diffusion equations. Zbl 0981.35023Poláčik, Peter; Yanagida, Eiji 3 2001 Structure of periodic solutions and asymptotic behavior for time-periodic reaction-diffusion equations on \(\mathbb{R}\). Zbl 0987.35079Feireisl, Eduard; Poláčik, Peter 21 2000 Realization of vector fields and dynamics of spatially homogeneous parabolic equations. Zbl 0926.35060Dancer, E. N.; Poláčik, P. 11 1999 Global nonexistence without blow-up for an evolution problem. Zbl 0938.35030Fila, Marek; Poláčik, Peter 8 1999 Global solutions of a semilinear parabolic equation. Zbl 0953.35065Fila, Marek; Poláčik, Peter 6 1999 Persistent saddle connections in a class of reaction-diffusion equations. Zbl 0936.35097Poláčik, Peter 2 1999 The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension. Zbl 0868.35062Brunovský, P.; Poláčik, P. 30 1997 On the local structure of \(\omega\)-limit sets of maps. Zbl 0889.34048Brunovský, P.; Poláčik, P. 12 1997 Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball. Zbl 0839.35059Chen, Xu-Yan; Poláčik, Peter 37 1996 Nonconvergent bounded trajectories in semilinear heat equations. Zbl 0845.35054Poláčik, Peter; Rybakowski, Krzysztof P. 32 1996 Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation. Zbl 0865.35065Poláčik, Peter; Šošovička, Vladimír 4 1996 High-dimensional \(\omega\)-limit sets and chaos in scalar parabolic equations. Zbl 0830.35060Poláčik, Peter 12 1995 Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations. Zbl 0822.35073Chen, Xu-Yan; Poláčik, Peter 11 1995 Imbedding vector fields in scalar parabolic Dirichlet BVPs. Zbl 0852.35074Poláčik, Peter; Rybakowski, Krzysztof 5 1995 Symmetry and convergence properties for nonnegative solutions of nonautonomous reaction-diffusion problems. Zbl 0811.35049Hess, Peter; Poláčik, P. 21 1994 Erratum to: Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0791.58008Poláčik, P.; Tereščák, I. 17 1994 Transversal and nontransversal intersections of stable and unstable manifolds in reaction diffusion equations on symmetric domains. Zbl 0809.35041Poláčik, Peter 6 1994 Realization of the dynamic of ODE’s in scalar parabolic PDEs. Zbl 0811.35065Poláčik, Peter 2 1994 Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations. Zbl 0786.58002Poláčik, P.; Tereščák, Ignác 49 1993 Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. Zbl 0797.58077Hess, Peter; Poláčik, Peter 17 1993 Convergence in general periodic parabolic equations in one space dimension. Zbl 0796.35009Brunovský, P.; Poláčik, P.; Sandstede, B. 29 1992 Convergence to a positive equilibrium for some nonlinear evolution equations in a ball. Zbl 0824.35011Haraux, A.; Poláčik, P. 20 1992 Imbedding of any vector field in a scalar semilinear parabolic equation. Zbl 0755.35046Poláčik, P. 8 1992 Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Zbl 0755.58039Poláčik, P.; Tereščák, I. 51 1991 Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. Zbl 0738.35027Poláčik, Peter 18 1991 Realization of any finite jet in a scalar semilinear parabolic equation on the ball in \(\mathbb{R}^ 3\). Zbl 0774.35041Poláčik, Peter 9 1991 Asymptotic behavior of solutions of semilinear elliptic equations on an unbounded strip. Zbl 0744.35013Brunovský, P.; Mora, X.; Poláčik, P.; Solà-Morales, J. 4 1991 Complicated dynamics of scalar reaction diffusion equations with a nonlocal term. Zbl 0726.35060Fiedler, Bernold; Poláčik, Peter 32 1990 Generic properties of strongly monotone semiflows defined by ordinary and parabolic differential equations. Zbl 0714.58043Poláčik, P. 2 1990 Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows. Zbl 0724.58054Poláčik, Peter 2 1990 Convergence in smooth strongly monotone flows defined by semilinear parabolic equations. Zbl 0684.34064Poláčik, Peter 42 1989 Domains of attraction of equilibria and monotonicity of convergent trajectories in parabolic systems admitting strong comparison principle. Zbl 0667.35036Poláčik, Peter 7 1989 Group actions on strongly monotone dynamical systems. Zbl 0642.58031Mierczyński, Janusz; Poláčik, Peter 6 1989 Generic hyperbolicity in one-dimensional reaction-diffusion equations with general boundary conditions. Zbl 0639.35039Poláčik, Peter 6 1987 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 943 Authors 53 Poláčik, Peter 32 Lou, Yuan 22 Shen, Wenxian 19 Wang, Yi 17 Yanagida, Eiji 15 Winkler, Michael 13 Fila, Marek 13 Peng, Rui 13 Wei, Juncheng 12 Matano, Hiroshi 12 Mizoguchi, Noriko 12 Souplet, Philippe 11 Du, Yihong 11 Obaya, Rafael 11 Quittner, Pavol 11 Weth, Tobias 10 Ishige, Kazuhiro 10 Lam, King-Yeung 10 Li, Wan-Tong 10 Lou, Bendong 10 Mierczyński, Janusz 10 Phan, Quoc Hung 10 Wang, Zhi Cheng 10 Zhao, Xiao-Qiang 9 Jendoubi, Mohamed Ali 9 Sanz, Ana M. 9 Villavert, John 9 Zhou, Maolin 8 Cantrell, Robert Stephen 8 Cosner, Chris 8 Dai, Wei 8 Guo, Zongming 8 Hamel, François 8 Jiang, Jifa 8 Yi, Taishan 8 Zou, Wenming 7 Chill, Ralph 7 Giletti, Thomas 7 Harrabi, Abdellaziz 7 Liu, Shuang 7 Shi, Junping 7 Smith, Hal Leslie 7 Valdebenito, Darío A. 7 Vishnevskii, Mikhail P. 6 Ding, Weiwei 6 Földes, Juraj 6 Kawakami, Tatsuki 6 Langa, Jose’ Antonio 6 Nadin, Grégoire 6 Peng, Shaolong 6 Qin, Guolin 6 Ruan, Shigui 6 Wang, Yuxia 6 Wu, Jianhua 6 Zhang, Zhitao 6 Zhou, Dun 5 Berestycki, Henri 5 Dancer, Edward Norman 5 Duong, Anh Tuan 5 Fiedler, Bernold 5 Giga, Yoshikazu 5 Grasselli, Maurizio 5 Huang, Haochuan 5 Huang, Rui 5 Jänig, Axel 5 Joly, Romain 5 Lin, Guo 5 Nolasco de Carvalho, Alexandre 5 Raugel, Geneviève 5 Rodríguez-Bernal, Aníbal 5 Roquejoffre, Jean-Michel 5 Vazquez, Juan Luis 5 Wang, Mingxin 5 Wu, Hao 5 Yang, Hui 5 Zhang, Liang 4 Alfaro, Matthieu 4 Bo, Wei-Jian 4 Brunovský, Pavol 4 Chen, Wenxiong 4 Cholewa, Jan W. 4 Del Pino, Manuel A. 4 Ducrot, Arnaud 4 Dupaigne, Louis 4 Farina, Alberto 4 Fujishima, Yohei 4 García-Melián, Jorge 4 Húska, Juraj 4 Kim, Yong Jung 4 Li, Congming 4 Li, Kui 4 Li, Yimei 4 Miyamoto, Yasuhito 4 Mtiri, Foued 4 Naito, Yūki 4 Rocha, Carlos 4 Saldaña, Alberto 4 Vétois, Jérôme 4 Wan, FangShu 4 Wang, Pengyan ...and 843 more Authors all top 5 Cited in 165 Serials 148 Journal of Differential Equations 52 Journal of Dynamics and Differential Equations 49 Journal of Mathematical Analysis and Applications 45 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 30 Calculus of Variations and Partial Differential Equations 30 Discrete and Continuous Dynamical Systems 23 Communications on Pure and Applied Analysis 21 Journal of Functional Analysis 19 Journal of Mathematical Biology 17 Transactions of the American Mathematical Society 16 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 16 Journal de Mathématiques Pures et Appliquées. Neuvième Série 16 Nonlinear Analysis. Real World Applications 16 Discrete and Continuous Dynamical Systems. Series B 15 Mathematische Annalen 15 Proceedings of the American Mathematical Society 13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 13 Communications in Contemporary Mathematics 12 Advances in Mathematics 12 Communications in Partial Differential Equations 11 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 NoDEA. Nonlinear Differential Equations and Applications 11 Journal of Evolution Equations 10 SIAM Journal on Mathematical Analysis 9 Archive for Rational Mechanics and Analysis 8 Nonlinearity 8 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Bulletin of Mathematical Biology 7 Advances in Difference Equations 7 Science China. Mathematics 7 Advances in Nonlinear Analysis 6 Siberian Mathematical Journal 6 Applied Mathematics Letters 5 Applicable Analysis 5 Journal d’Analyse Mathématique 5 Memoirs of the American Mathematical Society 5 Journal of Difference Equations and Applications 5 Complex Variables and Elliptic Equations 5 Journal of Biological Dynamics 5 Discrete and Continuous Dynamical Systems. Series S 4 Mathematical Biosciences 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Acta Applicandae Mathematicae 4 SIAM Journal on Applied Mathematics 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Electronic Journal of Differential Equations (EJDE) 4 Advanced Nonlinear Studies 4 Milan Journal of Mathematics 4 Mathematical Biosciences and Engineering 4 Boundary Value Problems 4 SN Partial Differential Equations and Applications 3 Communications in Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 Chaos, Solitons and Fractals 3 Archiv der Mathematik 3 Journal of Computational and Applied Mathematics 3 Physica D 3 Journal of Nonlinear Science 3 Topological Methods in Nonlinear Analysis 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Journal of Fixed Point Theory and Applications 3 Journal of Elliptic and Parabolic Equations 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 Methods in the Applied Sciences 2 Mathematical Notes 2 Journal of Geometry and Physics 2 Acta Mathematica 2 Journal of the Korean Mathematical Society 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Mathematische Zeitschrift 2 Monatshefte für Mathematik 2 Pacific Journal of Mathematics 2 Quarterly of Applied Mathematics 2 Tôhoku Mathematical Journal. Second Series 2 Chinese Annals of Mathematics. Series B 2 Journal of Integral Equations and Applications 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 2 Revista Matemática Complutense 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Nonlinear Science and Numerical Simulation 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Proceedings of the Steklov Institute of Mathematics 2 Analysis & PDE 2 Analysis and Mathematical Physics 2 Electronic Research Archive 1 Communications on Pure and Applied Mathematics 1 Journal of Statistical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Applied Mathematics and Computation 1 Automatica ...and 65 more Serials all top 5 Cited in 32 Fields 811 Partial differential equations (35-XX) 189 Biology and other natural sciences (92-XX) 146 Dynamical systems and ergodic theory (37-XX) 74 Ordinary differential equations (34-XX) 36 Operator theory (47-XX) 29 Integral equations (45-XX) 24 Global analysis, analysis on manifolds (58-XX) 12 Numerical analysis (65-XX) 12 Fluid mechanics (76-XX) 9 Functional analysis (46-XX) 9 Differential geometry (53-XX) 9 Systems theory; control (93-XX) 8 Difference and functional equations (39-XX) 7 Real functions (26-XX) 7 Potential theory (31-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Probability theory and stochastic processes (60-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 General topology (54-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Mechanics of particles and systems (70-XX) 5 Mechanics of deformable solids (74-XX) 4 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) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) Citations by Year