Multiplicity of positive solution for Schrödinger-Poisson system with \(p\)-Laplacian. (English) Zbl 1523.35024
Summary: In this paper, we consider the positive solutions for a Schrödinger-Poisson system containing p-Laplacian and Poisson equation. With a local condition on the potential, by using penalization method, Nehari manifold and Ljusternik-Schnirelmann category theory, the multiplicity and concentration of solutions are obtained.
MSC:
| 35B25 | Singular perturbations in context of PDEs |
| 35B09 | Positive solutions to PDEs |
| 35J47 | Second-order elliptic systems |
| 35J62 | Quasilinear elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
Keywords:
Schrödinger-Poisson system; \(p\)-Laplacian; variational methods; Ljusternik-Schnirelmann theoryReferences:
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