EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR KIRCHHOFF-SCHRODINGER-POISSON SYSTEM WITH CONCAVE AND CONVEX NONLINEARITIES

被引：4

作者：

Che, Guofeng ^{[1
]}

Chen, Haibo ^{[2
]}

机构：

[1] Guangdong Univ Technol, Sch Appl Math, Guangzhou 510006, Guangdong, Peoples R China

[2] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2020年 / 57卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Kirchhoff-Schriidinger-Poisson system; concave and convex nonlinearities; Mountain Pass Theorem; Ekeland's variational principle; GROUND-STATE SOLUTIONS; SIGN-CHANGING SOLUTIONS; POSITIVE SOLUTIONS; EQUATION;

D O I：

10.4134/JKMS.j190833

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the following Kirchhoff-Schriidinger-Poisson system {-(a+b integral(R3 )vertical bar del u vertical bar(2)dx)Delta u + V(x)u + mu phi u =lambda f(x)vertical bar u vertical bar(p-2)u + g(x)vertical bar u vertical bar(q-2)u, in R-3, -Delta phi = mu vertical bar u vertical bar(2), in R-3,R- where a > 0, b, mu >= 0, p is an element of [1,2), lambda E [4,6) and A > 0 is a parameter. Under some suitable assumptions on V(x), f(x) and g(x), we prove that the above system has at least two different nontrivial solutions via the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Some recent results from the literature are improved and extended.

引用

页码：1551 / 1571

页数：21

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