MULTIPLE POSITIVE SOLUTIONS FOR SCHRODINGER-POISSON SYSTEM IN R3 INVOLVING CONCAVE-CONVEX NONLINEARITIES WITH CRITICAL EXPONENT

被引：12
|
作者：
Li, Miao-Miao [1 ]
Tang, Chun-Lei [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2017年 / 16卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Schrodinger-Poisson system; Mountain Pass Theorem; Ekeland's variational principle; critical exponent; concentration compactness principle; SEMILINEAR ELLIPTIC-EQUATIONS; THOMAS-FERMI; R-N; ATOMS;
D O I：
10.3934/cpaa.2017076
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence of multiple positive solutions of the following Schrodinger-Poisson system with critical exponent { -Delta u - l(x)phi u = lambda h(x)vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(4)u, in R-3, -Delta phi = l(x)u(2), in R-3, where 1 < q < 2 and lambda > 0. Under some appropriate conditions on l and h, we show that there exists lambda* > 0 such that the above problem has at least two positive solutions for each lambda is an element of (0, lambda*) by using the Mountain Pass Theorem and Ekeland's Variational Principle.
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页码：1587 / 1602
页数：16
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