Existence of nontrivial solutions for fractional Schrodinger-Poisson system with sign-changing potentials

被引：7

作者：

Che, Guofeng ^{[1
]}

Chen, Haibo ^{[1
]}

Shi, Hongxia ^{[2
]}

Wang, Zewei ^{[3
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Hunan First Normal Univ, Sch Math & Computat Sci, Changsha 410205, Hunan, Peoples R China

[3] Sun Yat Sen Univ, Sch Earth Sci & Engn, Guangzhou 510275, Guangdong, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 13期

基金：

中国国家自然科学基金;

关键词：

fractional Schrodinger-Poisson system; nodal solution; positive solution; variational methods; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; ENERGY SOLUTIONS; NODAL SOLUTIONS; BOUND-STATES; EQUATIONS; MULTIPLICITY;

D O I：

10.1002/mma.4951

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 fractional Schrodinger-Poisson system {(-Delta)alpha u+ V(x)u + K(x)phi u = f(x)vertical bar u vertical bar q-2u, in R-3 (-Delta)t phi = K(x)u2, in R3 where 0< t= a< 1, q. o4; 2* athorn, and 4a+ 2t= 3 and the functions V(x), K(x) and f(x) have finite limits as | x|.8. By imposing some suitable conditions on the decay rate of the functions, we prove that the above system has two nontrivial solutions. One of them is positive and the other one is sign-changing. Recent results from the literature are generally improved and extended.

引用

页码：5050 / 5064

页数：15

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