带p-Laplacian算子的哈密顿系统同宿解的研究

Research on Homoclinic Solution of Hamiltonian System with p-Laplacian Operator

本文研究一类带p-Laplacian算子的哈密顿系统可解性的问题.在势函数W(t,u)满足新的超p次和次p次增长组合条件时,利用临界点理论得到上述系统同宿解的存在性定理,推广了相关问题已有的结果.

This paper studies the solvability of a class of Hamiltonian systems with p-Laplacian operators.When the potential function W(t,u)satisfies the new combination of super p-th and sub p-th growth conditions,the critical point theory is used to obtain the existence theorem of the homoclinic solution of the above system,which extends the existing results of related problems.