Existence of homoclinic solution in first order discrete Hamiltonian system

2014/08/26 by Chen, Wenxiong
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1408.6016

Abstract

In this paper we consider the first order discrete Hamiltonian system \begincases x₁(n+1)-x₁(n)amp; =- H_x2(n,x(n)), x₂(n)-x₂(n-1)amp; = H_x1(n,x(n)). \endcases Where n∈ ℤ, x(n)= x₁ (n) \choose x₂ (n) ∈ ℝ^2N, H(n,z)= \frac12S(n)z⋅ z + R(n,z) is periodic in n and asymptotically quadratic as |z| → ∞. We will prove the existence of homoclonic solution by critical point theorem for strongly indefinite functional.

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