二阶非线性差分方程正解的多重性  

Multiplicity of Solutions of Second-Order Nonlinear Difference Equations

作　　者：赵倩茹[1] 张建明[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2012年第1期60-62,共3页Journal of North University of China(Natural Science Edition)

基　　金：山西省自然科学基金资助项目(2011011002-4)

摘　　要：得到了一类带参数的二阶非线性差分方程(Pλ)的变分结构,证明了问题(Pλ)的解等价于泛函Jλ在Banach空间H上的临界点.应用有限维Banach空间上的临界点理论和抽象的临界点定理研究了(Pλ)解的多重性,证明了当参数在某个开区间上时,(Pλ)至少存在3个不同的正解.The variational framework corresponding to a class of the second-order nonlinear difference equations（Pλ） with the parameters was obtained.It was proved that the solutions of the problem（Pλ） were equivalent to the critical points of the functional（Jλ） in Banach space H.By appling critical point theorem in the setting of finite dimensional Banach space,the multiplicity of solutions for（Pλ） was investigated.It is proved that,for every λ belonging to a well defined open interval,the problem（Pλ） has at least three distinct positive solutions.

关 键 词：差分方程 正解 有限维空间 临界点理论 

分 类 号：O177.91[理学—数学]