一类超线性离散薛定谔系统的基态解  

Ground state solutions for discrete Schrdinger systems with superlinear nonlinearties

作　　者：周阳锋[1] 沈自飞[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2011年第4期372-378,共7页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(10971194)

摘　　要：研究了离散薛定谔系统{-Δun+εnun=g(n,vn),-Δvn+εnvn=f(n,un)基态解的存在性.其中:-Δun=un+1+un-1-2un是一维空间的离散拉普拉斯算子;给定的序列{εn}关于n是k-周期的.通过弱环绕定理和集中紧性原理得到了不含Ambrosetti-Rabinowitz条件时系统基态解的存在性.类似的方法可以用来研究单个的离散薛定谔方程基态解的存在性.It was considered the following discrete Schrdinger systems{-Δun＋εnun=g（n,vn）,-Δvn＋εnvn=f（n,un）,where-Δun=un＋1＋un-1-2un denoted the discrete Laplacian in one spatial dimension and the given sequences {εn} was assumed to be k-periodic in n.The existence of ground state solutions without the classical Ambrosetti-Rabinowitz condition was established by a weak linking theorem and concentration compactness analysis.The same method could also be applied to obtain ground state solutions for single discrete nonlinear Schdinger systems.

关 键 词：离散薛定谔系统 基态解 弱环绕 集中紧性原理 

分 类 号：O175.2[理学—数学]