Existence and asymptotic behaviour of solutions for a quasi-linear Schrodinger-Poisson system with a critical nonlinearity

被引：22
|
作者：
Figueiredo, Giovany M. [1 ]
Siciliano, Gaetano [2 ]
机构：
[1] Univ Brasilia UNB, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
[2] Univ Sao Paulo, Dept Matemat, Rua Matao 1010, BR-05508009 Sao Paulo, SP, Brazil
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2020年 / 71卷 / 04期
基金：
巴西圣保罗研究基金会;
关键词：
Variational methods; Nonlocal problems; Schrodinger-Poisson equation; Critical growth; STANDING WAVES; POSITIVE SOLUTIONS; EQUATIONS; STABILITY;
D O I：
10.1007/s00033-020-01356-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the following quasilinear Schrodinger-Poisson system {-Delta u + u +phi u = lambda f(x, u) + vertical bar u vertical bar(4)u on R-3 {-Delta phi + epsilon(4) Delta(4)phi = u(2) in R-3,R- depending on the two parameters lambda epsilon > 0. We first prove that, for. larger than a certain lambda* > 0, there exists a solution for every epsilon > 0. Later, we study the asymptotic behaviour of these solutions whenever epsilon tends to zero, and we prove that they converge to the solution of the Schrodinger-Poisson system associated.
引用
收藏
页数：21
相关论文
共 50 条
12345