Infinitely many dichotomous solutions for the Schrödinger-Poisson system  

作　　者：Yuke He Benniao Li Wei Long 

机构地区：[1]School of Mathematics and Statistics and Jiangxi Provincial Center for Applied Mathematics,Jiangxi Normal University,Nanchang 330022,China

出　　处：《Science China Mathematics》2024年第9期2049-2070,共22页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12101274 and 12226309);the Jiangxi Province Science Fund for Distinguished Young Scholars(Grant No.20224ACB218001);supported by National Natural Science Foundation of China(Grant No.12271223);Jiangxi Provincial Natural Science Foundation(Grant No.20212ACB201003);Jiangxi Two Thousand Talents Program(Grant No.jxsq2019101001);Double-high Talents Program in Jiangxi Province。

摘　　要：In this paper,we consider the following Schrodinger-Poisson system{-ε^(2)Δu+V(x)u+K(x)Φ(x)u=|u|^(p-1)u in R^(N),-ΔΦ(x)=K(x)u^(2)in RN,,where e is a small parameter,1<p<N+2/N-2,N∈[3,6],and V(x)and K(x)are potential functions with different decay at infinity.We first prove the non-degeneracy of a radial low-energy solution.Moreover,by using the non-degenerate solution,we construct a new type of infinitely many solutions for the above system,which are called“dichotomous solutions”,i.e.,these solutions concentrate both in a bounded domain and near infinity.

关 键 词：dichotomous solutions NON-DEGENERACY Schrodinger-Poisson system 

分 类 号：O175.29[理学—数学]