Existence and multiplicity results for some Schrodinger-Poisson system with critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:488

Article

Li, Na¹  He, Xiaoming¹ 

[1] Minzu Univ China, Sch Sci, Beijing 100081, Peoples R China

关键词: Schrodinger-Poisson system;    Ljusternik-Schnirelmann theory;    Nehari manifold;    Critical Sobolev exponent;   

DOI  :  10.1016/j.jmaa.2020.124071

来源: Elsevier

【 摘 要 】

In this paper we study the existence and multiplicity of positive solutions for the Schriidinger-Poisson system with critical growth: {-epsilon(2)Delta u + V (x)u = f (u) + vertical bar u vertical bar(3)u phi, x is an element of R-3, -epsilon(2)Delta phi = vertical bar u vertical bar(5), x is an element of R-3, u is an element of H-1 (R-3), u(x) > 0, x is an element of R-3, where epsilon > 0 is a parameter, V : R-3 -> R is a continuous function and f : R -> R is a C-1 function. Under a global condition for V we prove that the above problem has a ground state solution and relate the number of positive solutions with the topology of the set where V attains its minimum, by using variational methods. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free