Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems

• 作者: Mohsen Timoumi
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: HAMILTONIAN Systems Partial NONLINEARITY Multiple PERIODIC Solutions Critical Point Theory
• 年，卷（期）: 2011,（7）
• 页码范围: 846-853
• 页数: 8页
• 分类号: O1

摘要

Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.