# Periodic solutions of an infinite dimensional hamiltonian system

Yanheng Ding, Cheng Lee

Research output: Contribution to journalArticle

14 Citations (Scopus)

### Abstract

We establish existence and multiplicity of periodic solutions to the infinite dimensional Hamiltonian system (∂tu - Δxu = Hv(t, x, u, v) -∂tu - Δxu = Hv(t, x, u, v) for (t, x) ∈R × Ω, where Ω ⊂ RN is a bounded domain or Ω = RN. When Ω is bounded, we treat the situations where H(t, x, z) is, with respect to z = (u, v), sub- or superquadratic, or concave and convex, and discuss also the convergence to homoclinics of sequences of subharmonic orbits. If Ω = RN, we handle the case of superquadratic nonlinearities.

Original language English 1881-1908 28 Rocky Mountain Journal of Mathematics 35 6 https://doi.org/10.1216/rmjm/1181069621 Published - 2005 Jan 1

### All Science Journal Classification (ASJC) codes

• Mathematics(all)
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