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