MULTIPLE SOLUTIONS FOR A NONHOMOGENEOUS SCHRODINGER-POISSON SYSTEM WITH CONCAVE AND CONVEX NONLINEARITIES

被引：3
作者：
Wang, Lixia [1 ,2 ]
Ma, Shiwang [3 ,4 ]
机构：
[1] Tianjin Univ, Ctr Appl Math, Weijin Rd, Tianjin 300072, Peoples R China
[2] Tianjin Chengjian Univ, Sch Sci, Jinjing Rd, Tianjin 300384, Peoples R China
[3] Nankai Univ, Sch Math Sci, Weijin Rd, Tianjin 300071, Peoples R China
[4] Nankai Univ, LPMC, Weijin Rd, Tianjin 300071, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Schrodinger-Poisson systems; concave and convex nonlinearities; variational methods; Ekeland's variational principle; Mountain Pass Theorem; GROUND-STATE SOLUTIONS; KLEIN-GORDON-MAXWELL; POSITIVE SOLUTIONS; SOLITARY WAVES; VARIATIONAL APPROACH; THOMAS-FERMI; EXISTENCE; EQUATIONS; ATOMS;
D O I：
10.11948/2156-907X.20180132
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 nonhomogeneous Schrodinger-Poisson equation (*) {-Delta u + V(x)u + phi(x)u = -k(x)vertical bar u vertical bar(q-2)u + h(x)vertical bar u vertical bar(p-2)u + g(x), 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, 4 < p < 6. Under some suitable assumptions on V(x), k(x), h(x) and g(x), the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.
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页码：628 / 637
页数：10
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