Multiplicity of Homoclinic Solutions for Second Order Hamiltonian Systems with Local Conditions at the Origin

• 作者: Peng LIU Fei GUO
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（4）
• 页码范围: 735-744
• 页数: 10页
• 语种: 英文

摘要

In this paper,the multiplicity of homoclinic solutions for second order non-autonomous Hamiltonian systems ü(t)-L(t)u(t)+▽uW(t,u(t))=0 is obtained via a new Symmetric Mountain Pass Lemma established by Kajikiya,where L ∈ C(R,RN×N)is symmetric but non-periodic,W ∈C1(R×RN,R)is locally even in u and only satisfies some growth conditions near u=0,which improves some previous results.