Existence of homoclinic solutions for some second-order discrete Hamiltonian systems

DOI10.1080/10236198.2012.666239zbMath1270.39004OpenAlexW2069424937MaRDI QIDQ4916374

Peng Chen, Xian Hua Tang

Publication date: 22 April 2013

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2012.666239

zbMATH Keywords

variational methodHamiltonian systemhomoclinic solutiondiscrete Hamiltonian systemsymmetric mountain pass theorem

Mathematics Subject Classification ID

Hamilton's equations (70H05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Discrete version of topics in analysis (39A12) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (14)

Standing wave solutions for the discrete nonlinear Schrödinger equations with indefinite sign subquadratic potentials ⋮ Existence of homoclinic orbits for fourth-order \(p\)-Laplacian difference equations ⋮ Existence theorems of periodic solutions for second-order difference equations containing both advance and retardation ⋮ Homoclinic solutions of 2\(n\)th-order difference equations containing both advance and retardation ⋮ Existence results of solitons in discrete non-linear Schrödinger equations ⋮ Existence and multiple solutions to a discrete fourth order boundary value problem ⋮ Homoclinic solutions for a class of fourth‐order difference equations ⋮ Nonexistence and existence results for a fourth-order \(p\)-Laplacian discrete Neumann boundary value problem ⋮ HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD ⋮ Existence of periodic solutions for a class of nonlinear difference equations ⋮ Periodic and subharmonic solutions for second-order nonlinear difference equations ⋮ Infinitely many homoclinic solutions for second-order discrete Hamiltonian systems ⋮ Existence of periodic solutions with prescribed minimal period of a \(2n\)th-order discrete system ⋮ Homoclinic orbits for second order \(p\)-Laplacian difference equations containing both advance and retardation

Cites Work

• Unnamed Item
• New existence of homoclinic orbits for a second-order Hamiltonian system
• A variational approach to homoclinic orbits in Hamiltonian systems
• Homoclinic orbits for second order self-adjoint difference equations
• Periodic and heteroclinic orbits for a periodic Hamiltonian system
• Homoclinic solutions for ordinary \(p\)-Laplacian systems with a coercive potential
• Weighted Sobolev spaces and the nonlinear Dirichlet problem in unbounded domains
• Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation
• Some results on connecting orbits for a class of Hamiltonian systems
• Homoclinic orbits and subharmonics for nonlinear second order difference equations
• Homoclinic solutions for a class of the second order Hamiltonian systems
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems
• Homoclinic orbits for a class of Hamiltonian systems
• Homoclinic solutions for a class of second-order Hamiltonian systems
• Homoclinic solutions for a class of second-order Hamiltonian systems
• Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential

This page was built for publication: Existence of homoclinic solutions for some second-order discrete Hamiltonian systems