带有一般位势退化拟线性Schrödinger方程的多解  

Infinitely Many Solutions of Degenerate Quasilinear Schrödinger Equations with General Potentials

作　　者：孟妍 黄先玖[1] 陈建华 MENG Yan;HUANG Xianjiu;CHEN Jianhua(School of Sciences,Nanchang University,Nanchang,Jiangxi,330031,P.R.China)

机构地区：[1]南昌大学理学院,南昌江西330031

出　　处：《数学进展》2022年第3期471-484,共14页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11661053,11771198,11961045,11901276);Provincial National Natural Science Foundation of Jiangxi(Nos.20181BAB201003,20202BAB201001,20202BAB211004).

摘　　要：本文主要研究下列拟线性Schrödinger方程-div(a(x,▽u))+V(x)|x|^(-2*α)u=K(x)|x|^(-2*α)f(x,u),x∈R^(N),其中N≥3,-∞<α<N-2/2,α≤e≤α+1,d=1+α-e,2*:=2*(α,e)=2N/N-2d(临界Hardy-Sobolev指数);V(x)和K(x)为非负的位势函数,函数a满足合适的条件;f在无穷远处超二次增长弱于Ambrosetti-Rabinowitz型条件.利用变分方法来研究拟线性Schr?dinger方程多解的存在性.In the present paper,we investigate the following quasilinear Schrodinger equation-div(a(x,▽u))+V(x)|x|^(-2*α)u=K(x)|x|^(-2*α)f(x,u),x∈R^(N),where N≥3,-∞<α<N-2/2,α≤e≤α+1,d=1+α-e and 2*:=2*(α,e)=2 N/N-2 d(the critical Hardy-Sobolev exponent);V(x)and K(x)are nonnegative potential functions;the function a satisfies suitable assumptions and the function f is of super-quadratic growth near infinity which is weaker than the Ambrosetti-Rabinowitz type condition.In view of the variational approach,we prove the existence of infinitely many nontrivial solutions for the quasilinear Schrodinger equation.

关 键 词：拟线性Schrodinger方程 超二次条件 多解 

分 类 号：O175.29[理学—数学]