时标上一类p-Laplacian哈密顿系统周期解的多重性

Multiplicity of Periodic Solutions for p-Laplacian Hamiltonian System on Time Scales

研究了形式如下的时标T上非自治的p-Laplacian哈密顿系统{(|u~Δ(t)|^(p-2)|u~Δ(t)|)~Δ=▽F(σ(t),u~σ(t)),Δ-几乎处处t∈[0,T]_(T^k),u(0)-u(T)=0,u~Δ(0)-u~Δ(T)=0的边值问题,运用三临界点定理,得到了哈密顿系统多个周期解的存在性定理.

In this paper,we studied a non-autonomous p-Laplacian Hamiltonian system on time scales T of the form {（｜u^Δ（t）｜^p-2｜u^Δ（t）｜）^Δ=▽F（σ（t）,u^σ（t））,Δ-a.e.t∈[0,T]T^k,u（0）-u（T）=0,u^Δ（0）-u^Δ（T）=0 The multiplicity of periodic solutions was obtained for this Hamiltonian system by means of the three critical point theorem.