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Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent

Authors :
Zheng Tian-Tian
Lei Chun-Yu
Liao Jia-Feng
Source :
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 584-592 (2024)
Publication Year :
2024
Publisher :
De Gruyter, 2024.

Abstract

In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type −Δu+u2∗1∣4πx∣u=μf(x)∣u∣p−2u+g(x)∣u∣4uinR3,-\Delta u+\left({u}^{2}\ast \frac{1}{| 4\pi x| }\right)u=\mu f\left(x){| u| }^{p-2}u+g\left(x){| u| }^{4}u\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{3}, where μ>0\mu \gt 0, 10\mu \gt 0 small; while gg has kk strict local maximum points, we prove that the equation has at least k+1k+1 distinct positive solutions for μ>0\mu \gt 0 small by the Nehari manifold. Moreover, we show that one of the solutions is a ground state solution.

Details

Language :
English
ISSN :
2191950X
Volume :
13
Issue :
1
Database :
Directory of Open Access Journals
Journal :
Advances in Nonlinear Analysis
Publication Type :
Academic Journal
Accession number :
edsdoj.4cdbf67b3b2a40188a754f24e8e68d25
Document Type :
article
Full Text :
https://doi.org/10.1515/anona-2023-0129