Nontrivial periodic solutions for strong resonance Hamiltonian systems via a local linking theorem

2011 ◽  
Vol 74 (16) ◽  
pp. 5467-5474
Author(s):  
Rong Cheng ◽  
Dongfeng Zhang
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Linking Theorem ◽  
Local Linking ◽  
Strong Resonance ◽  
Nontrivial Periodic Solutions

scholarly journals Periodic Solutions for Second Order Hamiltonian Systems with Impulses via the Local Linking Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Longsheng Bao ◽  
Binxiang Dai
Keyword(s):  
Periodic Solution ◽  
Hamiltonian System ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Second Order ◽  
Linking Theorem ◽  
Local Linking ◽  
Second Order Hamiltonian Systems ◽  
New Criterion

A class of second order impulsive Hamiltonian systems are considered. By applying a local linking theorem, we establish the new criterion to guarantee that this impulsive Hamiltonian system has at least one nontrivial T-periodic solution under local superquadratic condition. This result generalizes and improves some existing results in the known literature.

scholarly journals Existence of multiple critical points for an asymptotically quadratic functional with applications

1996 ◽  
Vol 1 (3) ◽  
pp. 277-289 ◽  
Author(s):  
Shujie Li ◽  
Jiabao Su
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Critical Points ◽  
Morse Theory ◽  
Quadratic Functional ◽  
Functional Applications ◽  
Critical Points At Infinity ◽  
Nontrivial Periodic Solutions

Morse theory for isolated critical points at infinity is used for the existence of multiple critical points for an asymptotically quadratic functional. Applications are also given for the existence of multiple nontrivial periodic solutions of asymptotically Hamiltonian systems.

Nonlinear problems with strong resonance at infinity: an abstract theorem and applications

1985 ◽  
Vol 99 (3-4) ◽  
pp. 333-345 ◽  
Author(s):  
A. Capozzi ◽  
A. Salvatore
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Wave Equations ◽  
Nonlinear Problems ◽  
Abstract Theorem ◽  
Semilinear Wave Equations ◽  
Strong Resonance ◽  
Image Position

SynopsisIn this paper, we consider the equationwhere A is a linear operator, N = ψ′ with ψ ∈ C1(E, R), and E is an Hilbert space. We suppose that N has a derivative at infinity N′(∞) and that 0 belongs to the spectrum of A–N′(∞). We prove an abstract theorem for multiplicity of solutions for the above equation. We then apply this theorem to the study of periodic solutions of Hamiltonian systems and of semilinear wave equations when the period is prescribed.

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