INFINITELY MANY SOLUTIONS FOR A SCHRODINGER-POISSON SYSTEM WITH CONCAVE AND CONVEX NONLINEARITIES

被引：21
|
作者：
Sun, Mingzheng [1 ,2 ]
Su, Jiabao [3 ]
Zhao, Leiga [4 ]
机构：
[1] Capital Normal Univ, Sch Math Sci, Beijing 100037, Peoples R China
[2] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China
[3] Capital Normal Univ, Sch Math Sci, Beijing 100037, Peoples R China
[4] Beijing Univ Chem Technol, Dept Math, Beijing 100029, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 01期
关键词：
Schrodinger-Poisson system; infinitely many solutions; concave and convex nonlinearities; nonlocal term; variational methods; POSITIVE SOLUTIONS; SOLITARY WAVES; MAXWELL; EXISTENCE; EQUATIONS;
D O I：
10.3934/dcds.2015.35.427
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we obtain the existence of infinitely many solutions for the following Schrodinger-Poisson system {-Delta u vertical bar a (x) u vertical bar phi u = k(x) vertical bar u vertical bar(q-2) u - h(x)vertical bar u vertical bar(p-2) u, x is an element of R-3; -Delta phi = u(2), lim(vertical bar x vertical bar -> +infinity) phi(x) = 0; x is an element of R-3, where 1 < q < 2 < p < +infinity, a (x), k (x) and h (x) are measurable functions satisfying suitable assumptions.
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页码：427 / 440
页数：14
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