离散共振问题的非平凡解  

Nontrivial Solutions of a Discrete Problem with Resonance

作　　者：尹莉莉[1] 刘进生[1] 

机构地区：[1]太原理工大学数学学院

出　　处：《数学的实践与认识》2012年第10期238-243,共6页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(2011011002-4)

摘　　要：研究了一类二阶非线性差分方程两点边值问题非平凡解的存在性.假设该问题在无穷远点及零点处均是共振的,利用变分方法,同时考虑正、负能量泛函的临界点,在一定的假设条件下,通过临界群的计算,证明了该问题至少存在一个非平凡解.In this paper,we study the existence of nontrivial solutions of a two-point boundary value problem of second-order nonlinear difference equations.By using variational method,considering critical points of both the positive and negative energy functional,when the problem is resonant both at infinity and origin,combined with the computation of the critical group,we prove the problem has at least one non-zero solution in certain assumptions.

关 键 词：离散 共振 变分方法 临界群 

分 类 号：O175.7[理学—数学]