The existence of homoclinic solutions for second-order Hamiltonian systems with periodic potentials

DOI10.1016/J.NONRWA.2011.03.019zbMath1343.37052OpenAlexW2081741357MaRDI QIDQ635235

Zhi-Qing Han, Ming-hai Yang

Publication date: 19 August 2011

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.03.019

zbMATH Keywords

mountain pass theoremhomoclinic solutionssecond-order Hamiltonian systemsgeneralized linking theorem

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (16)

Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems ⋮ Fast homoclinic solutions for damped vibration problems with superquadratic potentials ⋮ On locally superquadratic Hamiltonian systems with periodic potential ⋮ Multiplicity of homoclinic solutions for second order Hamiltonian systems with local conditions at the origin ⋮ Homoclinic solutions for \(p(t)\)-Laplacian-Hamiltonian systems without coercive conditions ⋮ On ground-state homoclinic orbits of a class of superquadratic damped vibration systems ⋮ Homoclinic solutions for \(p\)-Laplacian Hamiltonian systems with combined nonlinearities ⋮ Existence of two almost homoclinic solutions for \(p(t)\)-Laplacian Hamiltonian systems with a small perturbation ⋮ Infinitely many homoclinic solutions for damped vibration problems with subquadratic potentials ⋮ Local super-quadratic conditions on homoclinic solutions for a second-order Hamiltonian system ⋮ Fast homoclinic orbits for a class of damped vibration systems ⋮ Infinitely many homoclinic solutions for a second-order Hamiltonian system with locally defined potentials ⋮ Multiple Homoclinic Solutions for Second‐Order Perturbed Hamiltonian Systems ⋮ Infinitely many homoclinic solutions for a second-order Hamiltonian system ⋮ Subharmonic and homoclinic solutions for second order Hamiltonian systems with new superquadratic conditions ⋮ TWO ALMOST HOMOCLINIC SOLUTIONS FOR A CLASS OF PERTURBED HAMILTONIAN SYSTEMS WITHOUT COERCIVE CONDITIONS

Cites Work

• Unnamed Item
• Infinitely many homoclinic solutions for second-order Hamiltonian systems with odd nonlinearities
• Existence and multiplicity of homoclinic orbits for the second order Hamiltonian systems
• Infinitely many homoclinic orbits for the second-order Hamiltonian systems with super-quadratic potentials
• Ground state solutions for some indefinite variational problems
• Existence of homoclinic solution for the second order Hamiltonian systems.
• Some results on connecting orbits for a class of Hamiltonian systems
• Nontrivial solutions for perturbations of the \(p\)-Laplacian on unbounded domains
• Homoclinic solutions for a class of systems of second order differential equations
• Minimax theorems
• Generalized linking theorem with an application to a semilinear Schrödinger equation
• Homoclinic solutions for a class of the second order Hamiltonian systems
• Homoclinic solutions for some second order non-autonomous Hamiltonian systems without the globally superquadratic condition
• Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• Variational elliptic problems which are nonquadratic at infinity
• Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems
• Homoclinic orbits for a class of Hamiltonian systems
• Homoclinic orbits for a class of Hamiltonian systems
• Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential

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