带有位势井的分数阶渐近薛定谔方程的多解性研究  

Multiple Solutions for Asymptotically Linear Fractional Schr?dinger Equation with Steep Potential Well

作　　者：陆伟东[1] 单远 Lu Weidong;Shan Yuan(School of Mathematics of Nanjing Audit University,Nanjing 211815,China)

机构地区：[1]南京审计大学数学学院,江苏南京211815

出　　处：《南京师大学报（自然科学版）》2023年第1期1-5,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971233)。

摘　　要：研究分数阶薛定谔方程:(-Δ)^(s)u+V_(λ)(x)u=f(x,u),0<s<1,x∈R^(N),其中N>2s,f满足渐近线性条件,且当λ充分大时位势函数Vλ具有位势井.利用临界点定理得到方程的多解性.In this paper,we study the nonlinear fractional Schrodinger equation(-Δ)^(s)u+V_(λ)(x)u=f(x,u),0<s<1,x∈R N,on the whole space R^(N) with N>2s.The nonlinearity f is assumed to be asymptotically linear and the potential Vλhas a steep potential well for sufficiently large parameterλ.By virtue of critical point theory,the existence of multiple solutions are obtained.

关 键 词：分数阶薛定谔方程 位势井 渐近线性条件 多解性 

分 类 号：O175.2[理学—数学]