Schrödinger-Poisson systems with singular potential and critical exponent

Date

2020-12-26

Authors

Liu, Senli
Chen, Haibo
Feng, Zhaosheng

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article we study the Schrödinger-Poisson system -Δu + V(|x|)u + λφu = ƒ(u), x ∈ ℝ3, -Δφ = u2, x ∈ ℝ3 where V is a singular potential with the parameter α and the nonlinearity ƒ satisfies critical growth. By applying a generalized version of Lions-type theorem and the Nehari manifold theory, we establish the existence of the nonnegative ground state solution when λ = 0. By the perturbation method, we obtain a nontrivial solution to above system when λ ≠ 0.

Description

Keywords

Schrödinger-Poisson system, Lions-type theorem, Singular potential, Ground state solution, Critical exponent

Citation

Liu, S., Chen, H., & Feng, Z. (2020). Schrödinger-Poisson systems with singular potential and critical exponent. <i>Electronic Journal of Differential Equations, 2020</i>(130), pp. 1-17.

Rights

Attribution 4.0 International

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