时标上一类非自治哈密顿系统周期解的存在性

Existence of Periodic Solutions for Non-Autonomous Hamiltonian System on Time Scales

研究时标!上一类非自治的p-Laplacian哈密顿系统{(|u~Δ(t)|p-2|u~Δ(t))~Δ=▽F(σ(t),u~σ(t)),Δ-a.e.t∈0[,T]_(T^(k)),u(0)-u(T)=0,u~Δ(0)-u~Δ(T)=0的周期边值问题.利用最小作用原理,得到该哈密顿系统周期解的存在性判定定理,并举例说明了定理的有效性.所得结果推广了相关文献的结论.

The authors studied a non-autonomous p-Laplacian Hamiltonian system on time scales Tof 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 existence of at least one periodic solution for this Hamiltonian system was obtained by the principle of least action which extended the associated results of the relevant literature. One example was given to illustrate the advantages of our main results.