Edit Profile (opens in new tab) Benci, Vieri Co-Author Distance Author ID: benci.vieri Published as: Benci, Vieri; Benci, V. External Links: MGP · ORCID · Google Scholar · ResearchGate · dblp Documents Indexed: 206 Publications since 1972, including 4 Books and 9 Additional arXiv Preprints 3 Contributions as Editor Co-Authors: 69 Co-Authors with 173 Joint Publications 1,081 Co-Co-Authors all top 5 Co-Authors 36 single-authored 72 Fortunato, Donato 15 Giannoni, Fabio 14 Micheletti, Anna Maria 11 Di Nasso, Mauro 10 Baglini, Lorenzo Luperi 8 Bonanno, Claudio 8 Menconi, Giulia 7 Masiello, Antonio 6 Cerami, Giovanna 6 Galatolo, Stefano 6 Ghimenti, Marco G. 5 Badiale, Marino 5 Bellazzini, Jacopo 5 Forti, Marco 5 Pisani, Lorenzo 4 D’Aprile, Teresa 4 Piccione, Paolo 3 Abbondandolo, Alberto 3 Capozzi, Alberto 3 Grisanti, Carlo-Romano 3 Horsten, Leon 3 Nardulli, Stefano 3 Rabinowitz, Paul Henry 3 Rolando, Sergio 3 Wenmackers, Sylvia 2 Bottazzi, Emanuele 2 Cerrai, Paola 2 Cococcioni, Marco 2 Degiovanni, Marco 2 Freguglia, Paolo 2 Gazzola, Filippo 2 Osorio Acevedo, Luis Eduardo 2 Pacella, Filomena 2 Sinibaldi, Edoardo 2 Squassina, Marco 2 Visetti, Daniela 1 Al-Gwaiz, Mohammed A. 1 Allegrini, Paolo 1 Ambrosetti, Antonio 1 Argenti, Fiorella 1 Azzollini, Antonio 1 Bartolo, Paolo 1 Berselli, Luigi Carlo 1 Buiatti, Marcello 1 Capoi, A. 1 Cordelli, Alessandro 1 Coron, Jean-Michel 1 Corona, Dario 1 d’Avenia, Pietro 1 de Rezende, Ketty Abaroa 1 Dell’Antonio, Gian Fausto 1 D’Onofrio, Biancamaria 1 Fiaschi, Lorenzo 1 Grigolini, Paolo 1 Hofer, Helmut H. W. 1 Ignaccolo, Massimiliano 1 Long, Yiming 1 Luperi, Lorenzo 1 Mosconi, Sunra J. N. 1 Nisoli, Isaia 1 Palatella, Luigi 1 Passaseo, Donato 1 Ponchio, Federico 1 Raffaelli, Giacomo 1 Scafetta, Nicola 1 Shteto, Edlira 1 Simonov, Kyrylo 1 Visciglia, Nicola 1 Yang, J. all top 5 Serials 9 Journal of Differential Equations 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Topological Methods in Nonlinear Analysis 7 Advanced Nonlinear Studies 6 Archive for Rational Mechanics and Analysis 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Nonlinear Analysis. Theory, Methods & Applications 4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 4 Milan Journal of Mathematics 3 Journal of Mathematical Analysis and Applications 3 Chaos, Solitons and Fractals 3 Proceedings of the American Mathematical Society 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Calculus of Variations and Partial Differential Equations 3 Bollettino della Unione Matematica Italiana. Series V. B 3 Journal of Fixed Point Theory and Applications 3 Discrete and Continuous Dynamical Systems. Series S 2 Communications on Pure and Applied Mathematics 2 Reviews in Mathematical Physics 2 Advances in Mathematics 2 Conferenze del Seminario di Matematica dell’Università di Bari 2 Journal of Functional Analysis 2 Mathematische Zeitschrift 2 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 2 Ricerche di Matematica 2 Advances in Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Dynamics of Partial Differential Equations 2 Advances in Nonlinear Analysis 1 Communications in Mathematical Physics 1 Journal of Mathematical Physics 1 Journal of Geometry and Physics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 The British Journal for the Philosophy of Science 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Logique et Analyse. Nouvelle Série 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Monatshefte für Mathematik 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Transactions of the American Mathematical Society 1 Rendiconti del Seminario Matematico 1 Ergodic Theory and Dynamical Systems 1 Annals of Pure and Applied Logic 1 Complex Systems 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Communications in Partial Differential Equations 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Expositiones Mathematicae 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Electronic Journal of Differential Equations (EJDE) 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 NoDEA. Nonlinear Differential Equations and Applications 1 Mathematical Research Letters 1 Arab Journal of Mathematical Sciences 1 Journal of the European Mathematical Society (JEMS) 1 International Journal of Applied Mathematics and Computer Science 1 Lettera Matematica Pristem 1 Discrete and Continuous Dynamical Systems. Series B 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Boletim da Sociedade Paranaense de Matemática. Terceira Série 1 Mediterranean Journal of Mathematics 1 Bollettino della Unione Matematica Italiana. Series IV 1 Rendiconti di Matematica, VI. Serie 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 Journal of Logic and Analysis 1 Journal of Theoretical Biology 1 Arabian Journal of Mathematics 1 Matematica, Cultura e Società. Rivista dell’Unione Matematica Italiana. Serie I 1 Progress in Nonlinear Differential Equations and Their Applications 1 Springer Monographs in Mathematics 1 Calcoli Sublimi all top 5 Fields 94 Partial differential equations (35-XX) 52 Global analysis, analysis on manifolds (58-XX) 42 Dynamical systems and ergodic theory (37-XX) 26 Real functions (26-XX) 24 Operator theory (47-XX) 21 Ordinary differential equations (34-XX) 21 Mechanics of particles and systems (70-XX) 19 Mathematical logic and foundations (03-XX) 17 Quantum theory (81-XX) 16 Differential geometry (53-XX) 15 Functional analysis (46-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 9 Information and communication theory, circuits (94-XX) 7 Probability theory and stochastic processes (60-XX) 7 Computer science (68-XX) 7 Relativity and gravitational theory (83-XX) 6 General topology (54-XX) 6 Optics, electromagnetic theory (78-XX) 5 General and overarching topics; collections (00-XX) 5 Measure and integration (28-XX) 4 Mechanics of deformable solids (74-XX) 2 History and biography (01-XX) 2 Field theory and polynomials (12-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 168 Publications have been cited 4,370 times in 2,860 Documents Cited by ▼ Year ▼ Abstract critical point theorems and applications to some nonlinear problems with ”strong” resonance at infinity. Zbl 0522.58012 Bartolo, P.; Benci, V.; Fortunato, D. 496 1983 An eigenvalue problem for the Schrödinger-Maxwell equations. Zbl 0926.35125 Benci, Vieri; Fortunato, Donato 452 1998 Critical point theorems for indefinite functionals. Zbl 0465.49006 Benci, Vieri; Rabinowitz, Paul H. 264 1979 Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations. Zbl 1037.35075 Benci, Vieri; Fortunato, Donato 263 2002 On critical point theory for indefinite functionals in the presence of symmetries. Zbl 0504.58014 Benci, Vieri 186 1982 Positive solutions of some nonlinear elliptic problems in exterior domains. Zbl 0635.35036 Benci, Vieri; Cerami, Giovanna 183 1987 Existence of positive solutions of the equation \(-\Delta u+a(x)u=u^{(N+2)/(N-2)}\) in \({\mathbb{R}}^ N\). Zbl 0705.35042 Benci, Vieri; Cerami, Giovanna 171 1990 The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems. Zbl 0727.35055 Benci, Vieri; Cerami, Giovanna 147 1991 Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology. Zbl 0822.35046 Benci, Vieri; Cerami, Giovanna 141 1994 Solitons in several space dimensions: Derrick’s problem and infinitely many solutions. Zbl 0973.35161 Benci, V.; D’Avenia, P.; Fortunato, D.; Pisani, L. 131 2000 Soliton like solutions of a Lorentz invariant equation in dimension 3. Zbl 0921.35177 Benci, Vieri; Fortunato, Donato; Pisani, Lorenzo 52 1998 A geometrical index for the group \(S^1\) and some application to the study of periodic solutions of ordinary differential equations. Zbl 0447.34040 Benci, Vieri 51 1981 Towards a unified field theory for classical electrodynamics. Zbl 1065.78004 Benci, Vieri; Fortunato, Donato 48 2004 A new approach to the Morse-Conley theory and some applications. Zbl 0778.58011 Benci, Vieri 48 1991 On the existence of multiple geodesics in static space-times. Zbl 0716.53057 Benci, V.; Fortunato, D.; Giannoni, F. 45 1991 Solitons and the electromagnetic field. Zbl 0930.35168 Benci, V.; Fortunato, D.; Masiello, A.; Pisani, L. 42 1999 On the number of the positive solutions of some nonlinear elliptic problems. Zbl 0838.35040 Benci, V.; Cerami, G.; Passaseo, D. 40 1991 On the existence of infinitely many geodesics on space-time manifolds. Zbl 0808.58016 Benci, Vieri; Fortunato, Donato 39 1994 Variational methods in nonlinear field equations. Solitary waves, hylomorphic solitons and vortices. Zbl 1312.35001 Benci, Vieri; Fortunato, Donato 37 2014 Bending and stretching energies in a rectangular plate modeling suspension bridges. Zbl 1288.35201 Al-Gwaiz, Mohammed; Benci, Vieri; Gazzola, Filippo 36 2014 Periodic solutions of Lagrangian systems on a compact manifold. Zbl 0605.58034 Benci, Vieri 35 1986 Existence and non existence of the ground state solution for the nonlinear Schrödinger equations with \(V(\infty)=0\). Zbl 1105.35112 Benci, Vieri; Grisanti, Carlo R.; Micheletti, Anna Maria 34 2005 Numerosities of labelled sets: A new way of counting. Zbl 1028.03042 Benci, Vieri; Di Nasso, Mauro 33 2003 Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems. Zbl 0588.35007 Benci, V. 33 1984 Weighted Sobolev spaces and the nonlinear Dirichlet problem in unbounded domains. Zbl 0422.35038 Benci, V.; Fortunato, D. 33 1979 On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds. Zbl 1130.58010 Benci, Vieri; Bonanno, Claudio; Micheletti, Anna Maria 30 2007 Existence of static solutions of the semilinear Maxwell equations. Zbl 1150.35078 Azzollini, Antonio; Benci, V.; D’Aprile, Teresa; Fortunato, Donato 29 2006 The nonlinear Klein-Gordon equation coupled with the Maxwell equations. Zbl 1042.78500 Benci, Vieri; Fortunato, Donato 29 2001 Existence of solutions for the nonlinear Schrödinger equation with \(V(\infty)=0\). Zbl 1231.35225 Benci, Vieri; Grisanti, Carlo R.; Micheletti, Anna Maria 29 2006 Some critical point theorems and applications. Zbl 0472.58009 Benci, Vieri 28 1980 A nonlinear elliptic equation with singular potential and applications to nonlinear field equations. Zbl 1149.35033 Badiale, Marino; Benci, Vieri; Rolando, Sergio 28 2007 The semiclassical limit of the nonlinear Schrödinger equation in a radial potential. Zbl 1060.35129 Benci, Vieri; D’Aprile, Teresa 28 2002 Normal modes of a Lagrangian system constrained in a potential well. Zbl 0561.58006 Benci, V. 27 1984 Discreteness conditions of the spectrum of Schrödinger operators. Zbl 0389.35016 Benci, V.; Fortunato, D. 26 1978 The dual method in critical point theory. Multiplicity results for indefinite functional. Zbl 0526.58013 Benci, Vieri; Fortunato, Donato 25 1982 An eigenvalue problem for a quasilinear elliptic field equation. Zbl 1157.35348 Benci, V.; Micheletti, A. M.; Visetti, D. 25 2002 Periodic solutions of Hamiltonian systems with superquadratic potential. Zbl 0632.34036 Benci, V.; Capozzi, A.; Fortunato, D. 24 1986 Alpha-theory: An elementary axiomatics for nonstandard analysis. Zbl 1038.26019 Benci, Vieri; Di Nasso, Mauro 23 2003 A note on the existence of multiple brake orbits. Zbl 0811.70015 Ambrosetti, Antonio; Benci, Vieri; Long, Yiming 22 1993 Solitary waves in the nolinear wave equation and in gauge theories. Zbl 1122.35121 Benci, Vieri; Fortunato, Donato 21 2007 Periodic solutions of prescribed energy for a class of Hamiltonian systems with singular potentials. Zbl 0689.34034 Benci, Vieri; Giannoni, Fabio 21 1989 An Aristotelian notion of size. Zbl 1114.03055 Benci, Vieri; Di Nasso, Mauro; Forti, Marco 20 2006 Non-Archimedean probability. Zbl 1411.60007 Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia 20 2013 On the existence of closed geodesics on noncompact Riemannian manifolds. Zbl 0789.53028 Benci, Vieri; Giannoni, Fabio 19 1992 The eightfold path to nonstandard analysis. Zbl 1104.03061 Benci, Vieri; Forti, Marco; Di Nasso, Mauro 19 2006 Solitons in Schrödinger-Maxwell equations. Zbl 1307.35292 Benci, Vieri; Fortunato, Donato 18 2014 Solitary waves with non-vanishing angular momentum. Zbl 1030.35051 Benci, Vieri; Visciglia, Nicola 18 2003 Homoclinic orbits on compact manifolds. Zbl 0737.58052 Benci, Vieri; Giannoni, Fabio 17 1991 On the existence of geodesics in static Lorentz manifolds with singular boundary. Zbl 0776.53040 Benci, V.; Fortunato, D.; Giannoni, F. 17 1992 Infinitesimal probabilities. Zbl 1400.03006 Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia 17 2018 Hylomorphic solitons in the nonlinear Klein-Gordon equation. Zbl 1194.35096 Bellazzini, J.; Benci, V.; Bonanno, C.; Sinibaldi, E. 16 2009 Positive solutions of some eigenvalue problems in the theory of variational inequalities. Zbl 0432.35059 Benci, Vieri 16 1977 Ultrafunctions and generalized solutions. Zbl 1273.26035 Benci, Vieri 16 2013 Periodic bounce trajectories with a low number of bounce points. Zbl 0667.34054 Benci, V.; Giannoni, F. 15 1989 Periodic solutions of asymptotically linear dynamical systems. Zbl 0821.34037 Benci, Vieri; Fortunato, Donato 15 1994 Spinning Q-balls for the Klein-Gordon-Maxwell equations. Zbl 1194.78009 Benci, Vieri; Fortunato, Donato 15 2010 Does bifurcation from the essential spectrum occur? Zbl 0471.35007 Benci, Vieri; Fortunato, Donato 15 1981 On a filtration problem through a porous medium. Zbl 0298.76049 Benci, Vieri 15 1974 Existence of geodesics for the Lorentz metric of a stationary gravitational field. Zbl 0697.58011 Benci, Vieri; Fortunato, Donato 15 1990 On the existence of the fundamental eigenvalue of an elliptic problem in \(\mathbb R^N\). Zbl 1136.47040 Bellazzini, J.; Benci, V.; Ghimenti, M.; Micheletti, A. M. 15 2007 Solitary waves in Abelian gauge theories. Zbl 1157.58005 Benci, Vieri; Fortunato, Donato 14 2008 Hylomorphic solitons. Zbl 1205.35040 Benci, Vieri 14 2009 Introduction to Morse theory. A new approach. Zbl 0823.58008 Benci, Vieri 14 1995 Compression and diffusion: a joint approach to detect complexity. Zbl 1038.37062 Allegrini, P.; Benci, V.; Grigolini, P.; Hamilton, P.; Ignaccolo, M.; Menconi, G.; Palatella, L.; Raffaelli, G.; Scafetta, N.; Virgilio, M.; Yang, J. 14 2003 Some compact embedding theorems for weighted Sobolev spaces. Zbl 0382.46018 Benci, V.; Fortunato, D. 14 1976 Solitons for the nonlinear Klein-Gordon equation. Zbl 1200.35248 Bellazzini, J.; Benci, V.; Bonanno, C.; Micheletti, A. M. 14 2010 Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations. Zbl 1194.35343 Benci, Vieri; Fortunato, Donato 13 2009 A “Birkhoff-Lewis” type result for a class of Hamiltonian systems. Zbl 0616.58014 Benci, Vieri; Fortunato, Donato 13 1987 On the geodesic connectedness of Lorentzian manifolds. Zbl 0807.53054 Benci, Vieri; Fortunato, Donato; Masiello, Antonio 12 1994 Solutions in exterior domains of null mass nonlinear field equations. Zbl 1114.35143 Benci, Vieri; Micheletti, Anna Maria 12 2006 Solitary waves: physical aspects and mathematical results. Zbl 1120.37045 Badiale, Marino; Benci, V.; Rolando, Sergio 11 2004 Dynamical systems and computable information. Zbl 1058.94512 Benci, V.; Bonanno, C.; Galatolo, S.; Menconi, G.; Virgilio, M. 11 2004 Three-dimensional vortices in Abelian gauge theories. Zbl 1173.81013 Benci, Vieri; Fortunato, Donato 11 2009 Estimate of the number of periodic solutions via the twist number. Zbl 0881.34063 Benci, Vieri; Fortunato, Donato 11 1997 Geodesics on static Lorentz manifolds with convex boundary. Zbl 0820.53050 Benci, V.; Fortunato, D.; Giannoni, F. 11 1992 A non-Archimedean algebra and the Schwartz impossibility theorem. Zbl 1321.46045 Benci, Vieri; Luperi Baglini, Lorenzo 11 2015 Ultrafunctions and applications. Zbl 1290.26038 Benci, Vieri; Baglini, Lorenzo Luperi 11 2014 On the existence of stable charged Q-balls. Zbl 1272.35173 Benci, Vieri; Fortunato, Donato 11 2011 A remark on the nodal regions of the solutions of some superlinear elliptic equations. Zbl 0686.35043 Benci, Vieri; Fortunato, Donato 10 1989 On asymptotically quadratic Hamiltonian systems. Zbl 0525.70021 Benci, V.; Capozzi, A.; Fortunato, D. 10 1983 An algebraic approach to nonstandard analysis. Zbl 0973.26017 Benci, V. 10 2000 The nonlinear Schrödinger equation: solitons dynamics. Zbl 1205.35287 Benci, Vieri; Ghimenti, Marco; Micheletti, Anna Maria 10 2010 Morse theory for symmetric functionals on the sphere and an application to a bifurcation problem. Zbl 0564.58011 Benci, Vieri; Pacella, Filomena 9 1985 The Dirichlet problem for harmonic maps from the disk into the Euclidean n-sphere. Zbl 0597.35022 Benci, V.; Coron, Jean-Michel 9 1985 Three dimensional vortices in the nonlinear wave equation. Zbl 1178.35263 Badiale, Marino; Benci, Vieri; Rolando, Sergio 9 2009 A new proof of the existence of a brake orbit. Zbl 0674.34034 Benci, Vieri; Giannoni, Fabio 8 1989 Su un problema di autovalori per disequazioni variazionali. Zbl 0324.49004 Benci, V.; Micheletti, Anna Maria 8 1976 Basic properties of ultrafunctions. Zbl 1318.26054 Benci, Vieri; Luperi Baglini, Lorenzo 8 2014 Periodic solutions of a class of Hamiltonian systems. Zbl 0509.34039 Benci, V.; Capozzi, A.; Fortunato, D. 7 1982 Remarks on topological solitons. Zbl 0892.35101 Benci, Vieri; Fortunato, Donato; Pisani, Lorenzo 7 1996 A Morse index for geodesics in static Lorentz manifolds. Zbl 0735.58011 Benci, Vieri; Masiello, Antonio 7 1992 Hylomorphic solitons and charged Q-balls: existence and stability. Zbl 1348.35048 Benci, Vieri; Fortunato, Donato 7 2014 A ring homomorphism is enough to get nonstandard analysis. Zbl 1062.03066 Benci, Vieri; Di Nasso, Mauro 7 2003 Elementary numerosity and measures. Zbl 1300.26018 Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro 7 2014 Generalized functions beyond distributions. Zbl 1331.26051 Benci, Vieri; Luperi Baglini, Lorenzo 7 2015 A model problem for ultrafunctions. Zbl 1292.26073 Benci, Vieri; Luperi, Lorenzo 7 2014 An elementary approach to stochastic differential equations using the infinitesimals. Zbl 1232.03060 Benci, Vieri; Galatolo, Stefano; Ghimenti, Marco 6 2010 Morse theory for \(C^ 1\)-functionals and Conley blocks. Zbl 0848.58009 Benci, Vieri; Giannoni, Fabio 6 1994 Information and dynamical systems: A concrete measurement on sporadic dynamics. Zbl 1001.37013 Argenti, Fiorella; Benci, Vieri; Cerrai, Paola; Cordelli, Alessandro; Galatolo, Stefano; Menconi, Giulia 6 2002 Some nonlinear elliptic problems with asymptotic conditions. Zbl 0404.35043 Benci, Vieri; Fortunato, Donato 6 1979 Lusternik-Schnirelman and Morse theory for the van der Waals-Cahn-Hilliard equation with volume constraint. Zbl 1490.35178 Benci, Vieri; Nardulli, Stefano; Acevedo, Luis Eduardo Osorio; Piccione, Paolo 3 2022 Non-standard analysis revisited: an easy axiomatic presentation oriented towards numerical applications. Zbl 1515.03232 Benci, Vieri; Cococcioni, Marco; Fiaschi, Lorenzo 1 2022 The algorithmic numbers in non-Archimedean numerical computing environments. Zbl 07439617 Benci, Vieri; Cococcioni, Marco 2 2021 The Euclidean universe. Zbl 1507.03107 Benci, Vieri 1 2021 Multiple solutions for the Van der Waals-Allen-Cahn-Hilliard equation with a volume constraint. Zbl 1437.35208 Benci, Vieri; Nardulli, Stefano; Piccione, Paolo 3 2020 Generalized solutions of variational problems and applications. Zbl 1414.26051 Benci, Vieri; Luperi Baglini, Lorenzo; Squassina, Marco 2 2020 How to measure the infinite. Mathematics with infinite and infinitesimal numbers. Zbl 1429.26001 Benci, Vieri; Di Nasso, Mauro 6 2019 The Caccioppoli ultrafunctions. Zbl 1434.46024 Benci, Vieri; Berselli, Luigi Carlo; Grisanti, Carlo Romano 2 2019 Mathematics and infinity. History and topicality of a problem. (La matematica e l’infinito. Storia e attualità di un problema.) Zbl 1425.00068 Benci, Vieri; Freguglia, Paolo 1 2019 Infinitesimal probabilities. Zbl 1400.03006 Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia 17 2018 Toward the discovery of infinitesimal numbers. Lessons of mathematical analysis exposed in a non-Archimedean field. (Alla scoperta dei numeri infinitesimi. Lezioni di analisi matematica esposte in un campo non-archimedeo.) Zbl 1405.26004 Benci, Vieri 2 2018 Existence of torsional solitons in a beam model of suspension bridge. Zbl 1373.35301 Benci, Vieri; Fortunato, Donato; Gazzola, Filippo 6 2017 Generalized solutions in PDEs and the Burgers’ equation. Zbl 1373.35083 Benci, Vieri; Luperi Baglini, Lorenzo 3 2017 A generalization of Gauss’ divergence theorem. Zbl 1350.26017 Benci, Vieri; Baglini, Lorenzo Luperi 4 2016 A topological approach to non-Archimedean mathematics. Zbl 1351.26046 Benci, Vieri; Baglini, Lorenzo Luperi 3 2016 Hylomorphic solitons for the Benjamin-Ono and the fractional KdV equations. Zbl 1345.35014 Benci, Vieri; Fortunato, Donato 1 2016 A non-Archimedean algebra and the Schwartz impossibility theorem. Zbl 1321.46045 Benci, Vieri; Luperi Baglini, Lorenzo 11 2015 Generalized functions beyond distributions. Zbl 1331.26051 Benci, Vieri; Luperi Baglini, Lorenzo 7 2015 Some applications of numerosities in measure theory. Zbl 1309.26028 Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro 2 2015 Hylomorphic solitons for the generalized KdV equation. Zbl 1333.35230 Benci, Vieri; Fortunato, Donato 1 2015 Variational methods in nonlinear field equations. Solitary waves, hylomorphic solitons and vortices. Zbl 1312.35001 Benci, Vieri; Fortunato, Donato 37 2014 Bending and stretching energies in a rectangular plate modeling suspension bridges. Zbl 1288.35201 Al-Gwaiz, Mohammed; Benci, Vieri; Gazzola, Filippo 36 2014 Solitons in Schrödinger-Maxwell equations. Zbl 1307.35292 Benci, Vieri; Fortunato, Donato 18 2014 Ultrafunctions and applications. Zbl 1290.26038 Benci, Vieri; Baglini, Lorenzo Luperi 11 2014 Basic properties of ultrafunctions. Zbl 1318.26054 Benci, Vieri; Luperi Baglini, Lorenzo 8 2014 Hylomorphic solitons and charged Q-balls: existence and stability. Zbl 1348.35048 Benci, Vieri; Fortunato, Donato 7 2014 Elementary numerosity and measures. Zbl 1300.26018 Benci, Vieri; Bottazzi, Emanuele; Di Nasso, Mauro 7 2014 A model problem for ultrafunctions. Zbl 1292.26073 Benci, Vieri; Luperi, Lorenzo 7 2014 Non-Archimedean probability. Zbl 1411.60007 Benci, Vieri; Horsten, Leon; Wenmackers, Sylvia 20 2013 Ultrafunctions and generalized solutions. Zbl 1273.26035 Benci, Vieri 16 2013 On the existence of hylomorphic vortices in the nonlinear Klein-Gordon equation. Zbl 1307.35169 Bellazzini, J.; Benci, V.; Bonanno, C.; Sinibaldi, E. 5 2013 A minimization method and applications to the study of solitons. Zbl 1263.47084 Benci, Vieri; Fortunato, Donato 6 2012 On the dynamics of solitons in the nonlinear Schrödinger equation. Zbl 1256.35129 Benci, Vieri; Ghimenti, Marco; Micheletti, Anna Maria 6 2012 Solitary waves and vortices in non-abelian gauge theories with matter. Zbl 1260.81160 Benci, Vieri; Bonanno, Claudio 5 2012 Axioms for non-Archimedean probability (NAP). Zbl 1330.60008 Wenmackers, Sylvia; Benci, Vieri; Horsten, Leon 4 2012 Existence of solitons in the nonlinear beam equation. Zbl 1407.74046 Benci, Vieri; Fortunato, Donato 3 2012 On the existence of stable charged Q-balls. Zbl 1272.35173 Benci, Vieri; Fortunato, Donato 11 2011 Hamiltonian formulation of the Klein-Gordon-Maxwell equations. Zbl 1221.35003 Benci, Vieri; Fortunato, Donato 1 2011 The nonlinear Schroedinger equation: existence, stability and dynamics of solitons. Zbl 1241.35186 Benci, Vieri; Ghimenti, Marco; Micheletti, Anna Maria 1 2011 Spinning Q-balls for the Klein-Gordon-Maxwell equations. Zbl 1194.78009 Benci, Vieri; Fortunato, Donato 15 2010 Solitons for the nonlinear Klein-Gordon equation. Zbl 1200.35248 Bellazzini, J.; Benci, V.; Bonanno, C.; Micheletti, A. M. 14 2010 The nonlinear Schrödinger equation: solitons dynamics. Zbl 1205.35287 Benci, Vieri; Ghimenti, Marco; Micheletti, Anna Maria 10 2010 An elementary approach to stochastic differential equations using the infinitesimals. Zbl 1232.03060 Benci, Vieri; Galatolo, Stefano; Ghimenti, Marco 6 2010 Hylomorphic solitons on lattices. Zbl 1205.37081 Benci, Vieri; Fortunato, Donato 6 2010 Hylomorphic solitons in the nonlinear Klein-Gordon equation. Zbl 1194.35096 Bellazzini, J.; Benci, V.; Bonanno, C.; Sinibaldi, E. 16 2009 Hylomorphic solitons. Zbl 1205.35040 Benci, Vieri 14 2009 Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations. Zbl 1194.35343 Benci, Vieri; Fortunato, Donato 13 2009 Three-dimensional vortices in Abelian gauge theories. Zbl 1173.81013 Benci, Vieri; Fortunato, Donato 11 2009 Three dimensional vortices in the nonlinear wave equation. Zbl 1178.35263 Badiale, Marino; Benci, Vieri; Rolando, Sergio 9 2009 Solitary waves in Abelian gauge theories. Zbl 1157.58005 Benci, Vieri; Fortunato, Donato 14 2008 On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds. Zbl 1130.58010 Benci, Vieri; Bonanno, Claudio; Micheletti, Anna Maria 30 2007 A nonlinear elliptic equation with singular potential and applications to nonlinear field equations. Zbl 1149.35033 Badiale, Marino; Benci, Vieri; Rolando, Sergio 28 2007 Solitary waves in the nolinear wave equation and in gauge theories. Zbl 1122.35121 Benci, Vieri; Fortunato, Donato 21 2007 On the existence of the fundamental eigenvalue of an elliptic problem in \(\mathbb R^N\). Zbl 1136.47040 Bellazzini, J.; Benci, V.; Ghimenti, M.; Micheletti, A. M. 15 2007 An Euclidean measure of size for mathematical universes. Zbl 1131.03029 Benci, Vieri; Di Nasso, Mauro; Forti, Marco 3 2007 Existence of static solutions of the semilinear Maxwell equations. Zbl 1150.35078 Azzollini, Antonio; Benci, V.; D’Aprile, Teresa; Fortunato, Donato 29 2006 Existence of solutions for the nonlinear Schrödinger equation with \(V(\infty)=0\). Zbl 1231.35225 Benci, Vieri; Grisanti, Carlo R.; Micheletti, Anna Maria 29 2006 An Aristotelian notion of size. Zbl 1114.03055 Benci, Vieri; Di Nasso, Mauro; Forti, Marco 20 2006 The eightfold path to nonstandard analysis. Zbl 1104.03061 Benci, Vieri; Forti, Marco; Di Nasso, Mauro 19 2006 Solutions in exterior domains of null mass nonlinear field equations. Zbl 1114.35143 Benci, Vieri; Micheletti, Anna Maria 12 2006 Existence of 3D-vortices in abelian gauge theories. Zbl 1167.35351 Fortunato, Donato; Benci, V. 3 2006 A unitarian approach to classical electrodynamics: the semilinear Maxwell equations. Zbl 1129.78002 Benci, Vieri; Fortunato, Donato 3 2006 Periodic orbits of a one-dimensional non-autonomous Hamiltonian system. Zbl 1104.37041 Bellazzini, J.; Benci, V.; Ghimenti, M. 1 2006 Existence and non existence of the ground state solution for the nonlinear Schrödinger equations with \(V(\infty)=0\). Zbl 1105.35112 Benci, Vieri; Grisanti, Carlo R.; Micheletti, Anna Maria 34 2005 A purely algebraic characterization of the hyperreal numbers. Zbl 1113.26028 Benci, Vieri; Di Nasso, Mauro 5 2005 Matter and electromagnetic fields: remarks on the dualistic and unitarian standpoints. Zbl 1091.47057 Benci, Vieri; Fortunato, Donato 1 2005 Towards a unified field theory for classical electrodynamics. Zbl 1065.78004 Benci, Vieri; Fortunato, Donato 48 2004 Solitary waves: physical aspects and mathematical results. Zbl 1120.37045 Badiale, Marino; Benci, V.; Rolando, Sergio 11 2004 Dynamical systems and computable information. Zbl 1058.94512 Benci, V.; Bonanno, C.; Galatolo, S.; Menconi, G.; Virgilio, M. 11 2004 Solitary waves in classical field theory. Zbl 1404.58028 Benci, V.; Fortunato, D. 6 2004 A strongly degenerate elliptic equation arising from the semilinear Maxwell equations. Zbl 1116.35319 Benci, Vieri; Fortunato, Donato 4 2004 Numerosities of labelled sets: A new way of counting. Zbl 1028.03042 Benci, Vieri; Di Nasso, Mauro 33 2003 Alpha-theory: An elementary axiomatics for nonstandard analysis. Zbl 1038.26019 Benci, Vieri; Di Nasso, Mauro 23 2003 Solitary waves with non-vanishing angular momentum. Zbl 1030.35051 Benci, Vieri; Visciglia, Nicola 18 2003 Compression and diffusion: a joint approach to detect complexity. Zbl 1038.37062 Allegrini, P.; Benci, V.; Grigolini, P.; Hamilton, P.; Ignaccolo, M.; Menconi, G.; Palatella, L.; Raffaelli, G.; Scafetta, N.; Virgilio, M.; Yang, J. 14 2003 A ring homomorphism is enough to get nonstandard analysis. Zbl 1062.03066 Benci, Vieri; Di Nasso, Mauro 7 2003 On the Morse inequalities for geodesics on Lorentzian manifolds. Zbl 1056.53042 Abbondandolo, A.; Benci, V.; Fortunato, D.; Masiello, A. 5 2003 Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations. Zbl 1037.35075 Benci, Vieri; Fortunato, Donato 263 2002 The semiclassical limit of the nonlinear Schrödinger equation in a radial potential. Zbl 1060.35129 Benci, Vieri; D’Aprile, Teresa 28 2002 An eigenvalue problem for a quasilinear elliptic field equation. Zbl 1157.35348 Benci, V.; Micheletti, A. M.; Visetti, D. 25 2002 Information and dynamical systems: A concrete measurement on sporadic dynamics. Zbl 1001.37013 Argenti, Fiorella; Benci, Vieri; Cerrai, Paola; Cordelli, Alessandro; Galatolo, Stefano; Menconi, Giulia 6 2002 Hausdorff nonstandard extensions. Zbl 1061.54018 Forti, Marco; Di Nasso, Mauro; Benci, Vieri 4 2002 Solitary waves and Bohmian mechanics. Zbl 1063.81040 Abbondandolo, Alberto; Benci, Vieri 4 2002 Solitons and Bohmian mechanics. Zbl 0994.35102 Benci, Vieri 2 2002 Variational and topological methods in the study of nonlinear phenomena. Papers from the international conference, Pisa, Italy, January–February 2000. Zbl 1009.00018 1 2002 The nonlinear Klein-Gordon equation coupled with the Maxwell equations. Zbl 1042.78500 Benci, Vieri; Fortunato, Donato 29 2001 An eigenvalue problem for a quasilinear elliptic field equation on \(\mathbb R^n\). Zbl 1109.35369 Benci, V.; Micheletti, A. M.; Visetti, D. 5 2001 Existence, multiplicity and concentration of bound states for a quasilinear elliptic field equation. Zbl 1006.35034 Badiale, Marino; Benci, Vieri; D’Aprile, Teresa 4 2001 Semiclassical limit for a quasilinear elliptic field equation: One-peak and multipeak solutions. Zbl 1012.35026 Badiale, Marino; Benci, Vieri; D’Aprile, Teresa 3 2001 Solitons in several space dimensions: Derrick’s problem and infinitely many solutions. Zbl 0973.35161 Benci, V.; D’Avenia, P.; Fortunato, D.; Pisani, L. 131 2000 An algebraic approach to nonstandard analysis. Zbl 0973.26017 Benci, V. 10 2000 Solitons and relativistic dynamics. Zbl 0973.35162 Benci, V.; Fortunato, D. 4 2000 On the existence of the impossible pilot wave. Zbl 0952.35112 Benci, V.; Fortunato, D. 1 2000 A variational problem for manifold valued functions. Zbl 0995.58011 Benci, Vieri; Giannoni, Fabio; Piccione, Paolo 1 2000 Solitons and the electromagnetic field. Zbl 0930.35168 Benci, V.; Fortunato, D.; Masiello, A.; Pisani, L. 42 1999 Existence of string-like solitons. Zbl 0935.37047 Benci, Vieri; Fortunato, Donato 1 1999 An eigenvalue problem for the Schrödinger-Maxwell equations. Zbl 0926.35125 Benci, Vieri; Fortunato, Donato 452 1998 Soliton like solutions of a Lorentz invariant equation in dimension 3. Zbl 0921.35177 Benci, Vieri; Fortunato, Donato; Pisani, Lorenzo 52 1998 Some properties of the spectral flow in semi-Riemannian geometry. Zbl 0928.53020 Benci, Vieri; Giannoni, Fabio; Masiello, Antonio 5 1998 Estimate of the number of periodic solutions via the twist number. Zbl 0881.34063 Benci, Vieri; Fortunato, Donato 11 1997 ...and 68 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,981 Authors 88 Papageorgiou, Nikolaos S. 86 Benci, Vieri 69 Tang, Xianhua 64 Tang, Chun-Lei 46 Alves, Claudianor Oliveira 40 Fortunato, Donato 39 Figueiredo, Giovany Malcher 36 Candela, Anna Maria 36 Rădulescu, Vicenţiu D. 35 Chen, Haibo 33 Salvatore, Addolorata 32 Miyagaki, Olimpio Hiroshi 32 Zou, Wenming 30 Ambrosio, Vincenzo 30 Chen, Sitong 30 Wu, Tsungfang 29 Su, Jiabao 27 Gasiński, Leszek 27 Giannoni, Fabio 24 Micheletti, Anna Maria 24 Siciliano, Gaetano 23 Bartolo, Rossella 23 Schechter, Martin 22 Ding, Yanheng 22 Furtado, Marcelo Fernandes 21 Cingolani, Silvia 21 Zhao, Leiga 20 Ghimenti, Marco G. 20 Masiello, Antonio 20 Yang, Minbo 19 Cerami, Giovanna 19 Ma, Shiwang 19 Maia, Liliane A. 19 Repovš, Dušan D. 19 Zhang, Fubao 19 Zhang, Jihui 18 Do Ó, João M. Bezerra 18 Li, Gongbao 18 Liang, Sihua 18 Zhao, Fukun 17 Azzollini, Antonio 17 He, Xiaoming 17 Mederski, Jarosław 17 Sánchez Caja, Miguel 16 d’Avenia, Pietro 16 Piccione, Paolo 16 Wang, Jun 16 Zhang, Jianjun 15 Bartsch, Thomas J. 15 Chen, Guanwei 15 Sun, Juntao 15 Wang, Zhi-Qiang 15 Zhou, Huan-Song 14 Clapp, Mónica 14 Li, Shujie 14 Liu, Zhisu 14 Pisani, Lorenzo 14 Pomponio, Alessio 14 Qin, Dongdong 14 Squassina, Marco 14 Szulkin, Andrzej 14 Tanaka, Kazunaga 14 Tang, Zhongwei 13 Badiale, Marino 13 Cao, Daomin 13 Capozzi, Alberto 13 Molica Bisci, Giovanni 13 Perera, Kanishka 13 Winkert, Patrick 13 Zhang, Binlin 12 Flores, José Luis 12 Gazzola, Filippo 12 Malchiodi, Andrea 12 Molle, Riccardo 12 Mugnai, Dimitri 12 Wu, Xingping 12 Yang, Jianfu 12 Zhang, Duanzhi 12 Zhang, Jian 11 Chen, Shangjie 11 Germinario, Anna Valeria 11 Liu, Chungen 11 Ou, Zengqi 11 Rolando, Sergio 11 Teng, Kaimin 11 Vannella, Giuseppina 11 Wang, Chunhua 11 Xu, Junxiang 11 Zhang, Jian 10 Baglini, Lorenzo Luperi 10 Bonanno, Claudio 10 Da Silva, Edcarlos Domingos 10 D’Aprile, Teresa 10 Di Nasso, Mauro 10 Lei, Chunyu 10 Liu, Zhaoli 10 Lv, Ying 10 Passaseo, Donato 10 Peng, Shuangjie 10 Pistoia, Angela ...and 1,881 more Authors all top 5 Cited in 314 Serials 241 Nonlinear Analysis. 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RACSAM 10 Journal of Applied Analysis and Computation 10 Journal of Function Spaces 9 Communications in Mathematical Physics 9 Results in Mathematics 8 Mathematische Annalen 8 Rendiconti del Circolo Matemàtico di Palermo. Serie II 8 Acta Applicandae Mathematicae 8 Acta Mathematicae Applicatae Sinica. English Series 8 Acta Mathematica Sinica. English Series 8 Journal of Elliptic and Parabolic Equations 7 Journal d’Analyse Mathématique 7 Applied Mathematics and Optimization 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Acta Mathematica Sinica. New Series 7 Journal of Dynamics and Differential Equations 7 Advances in Differential Equations 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Synthese 6 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 6 Revista Matemática Iberoamericana 6 Asymptotic Analysis 6 Potential Analysis 6 Journal of Dynamical and Control Systems 6 Discrete and Continuous Dynamical Systems. Series B 6 Frontiers of Mathematics in China 6 Analysis and Mathematical Physics 6 Open Mathematics 6 Minimax Theory and its Applications 5 Israel Journal of Mathematics 5 Archiv der Mathematik 5 Inventiones Mathematicae 5 Journal of Computational and Applied Mathematics 5 Journal of the Korean Mathematical Society 5 Bulletin des Sciences Mathématiques 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Bulletin of the Brazilian Mathematical Society. New Series 5 Boletim da Sociedade Paranaense de Matemática. Terceira Série 5 The Review of Symbolic Logic ...and 214 more Serials all top 5 Cited in 56 Fields 2,113 Partial differential equations (35-XX) 625 Global analysis, analysis on manifolds (58-XX) 330 Ordinary differential equations (34-XX) 293 Dynamical systems and ergodic theory (37-XX) 245 Operator theory (47-XX) 148 Calculus of variations and optimal control; optimization (49-XX) 137 Differential geometry (53-XX) 119 Mechanics of particles and systems (70-XX) 96 Quantum theory (81-XX) 69 Optics, electromagnetic theory (78-XX) 66 Functional analysis (46-XX) 52 Mathematical logic and foundations (03-XX) 49 Real functions (26-XX) 41 Mechanics of deformable solids (74-XX) 35 Difference and functional equations (39-XX) 26 Relativity and gravitational theory (83-XX) 25 Fluid mechanics (76-XX) 23 Numerical analysis (65-XX) 21 Algebraic topology (55-XX) 20 Statistical mechanics, structure of matter (82-XX) 18 Integral equations (45-XX) 17 Probability theory and stochastic processes (60-XX) 17 Computer science (68-XX) 16 Biology and other natural sciences (92-XX) 14 Measure and integration (28-XX) 13 General and overarching topics; collections (00-XX) 11 Manifolds and cell complexes (57-XX) 10 Potential theory (31-XX) 10 Information and communication theory, circuits (94-XX) 9 General topology (54-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 History and biography (01-XX) 6 Combinatorics (05-XX) 5 Topological groups, Lie groups (22-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Systems theory; control (93-XX) 4 Number theory (11-XX) 4 Field theory and polynomials (12-XX) 4 Convex and discrete geometry (52-XX) 4 Operations research, mathematical programming (90-XX) 3 Special functions (33-XX) 3 Statistics (62-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 2 Astronomy and astrophysics (85-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 \(K\)-theory (19-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) Citations by Year