Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems

2011/06/02 by Chungen Lıu, Liu, Chungen, Qingye Zhang +1
Mathematics · #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1106.0361

openalex publication_date 2011/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system u-L(t)u(t)+W_u(t,u)=0, ∀ t∈ℝ, by means of the minmax arguments in the critical point theory, where L(t) is unnecessary uniformly positively definite for all t∈ ℝ and W_u(t, u) sastisfies the asymptotically linear condition.

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