On Schrodinger-Poisson systems involving concave-convex nonlinearities via a novel constraint approach

被引：15

作者：

Sun, Juntao ^{[1
]}

Wu, Tsung-Fang ^{[2
]}

机构：

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255049, Peoples R China

[2] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2021年 / 23卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Positive solutions; Schrodinger-Poisson systems; concave and convex nonlinearities; variational methods; POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; MULTIPLICITY; EXISTENCE;

D O I：

10.1142/S0219199720500480

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the multiplicity of positive solutions for a class of Schrodinger-Poisson systems with concave and convex nonlinearities as follows: {-Delta u + lambda V(x)u + mu phi u = a(x)vertical bar u vertical bar(p-2)u + b(x)vertical bar u vertical bar(q-2)u in R-3, -Delta phi = u(2) in R-3, where lambda, mu > 0 are two parameters, 1 < q < 2 < p < 4, V is an element of C(R-3) is a potential well, a is an element of L-infinity(R-3) and b is an element of Lp/(p-q)(R-3). Such problem cannot be studied by applying variational methods in a standard way, since the (PS) condition is still unsolved on H-1(R-3) due to 2 < p < 4. By developing a novel constraint approach, we prove that the above problem admits at least two positive solutions.

引用

页数：25