河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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时标上一类p-Laplacian哈密顿系统周期解的多重性

徐州工程学院数学与物理科学学院, 江苏徐州 221111
DOI： 10.13763/j.cnki.jhebnu.nse.2016.06.002

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

SU Ying, XUE Yimin

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摘要/Abstract

摘要：

研究了形式如下的时标J上非自治的p-Laplacian哈密顿系统（|u^Δ（t）|^p-2|u^Δ（t）|）^Δ=ΔF（σ（t），u^σ（t）），Δ几乎处处t∈[0，T]_J^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.

Abstract：

In this paper, we studied a non-autonomous p-Laplacian Hamiltonian system on time scales J of the form (|u^Δ(t)|^p-2|u^Δ(t)|)^Δ=ΔF(σ(t),u^σ(t)),Δ-a.e.t∈[0,T]_J^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.

关键词

关键词： 时标 ; p-Laplacian哈密顿系统 ; 周期解 ; 三临界点定理

Key words： time scales ; p-Laplacian Hamiltonian system ; periodic solution ; three critical point theorem

参考文献 19

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