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2019 Multiple solutions for Schrödinger-Poisson systems with critical nonlocal term
Zuji Guo
Topol. Methods Nonlinear Anal. 54(2A): 495-513 (2019). DOI: 10.12775/TMNA.2019.077

Abstract

This paper is concerned with the existence of positive bound state solutions for Schrödinger-Poisson systems with critical nonlocal term: \begin{equation} \begin{cases} -\Delta u=\phi|u|^{3}u+\lambda Q(x)|u|^{q-2}u &\text{in } \mathbb{R}^3, \\ -\Delta \phi=|u|^5 & \text{in } \mathbb{R}^3. \end{cases} \tag{$\mathcal{P}$} \end{equation} Under certain assumptions on $Q$ and $\lambda$, we prove that $(\mathcal{P})$ has multiple positive bound state solutions by decomposition the Nehari manifold and fine estimates.

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Zuji Guo. "Multiple solutions for Schrödinger-Poisson systems with critical nonlocal term." Topol. Methods Nonlinear Anal. 54 (2A) 495 - 513, 2019. https://doi.org/10.12775/TMNA.2019.077

Information

Published: 2019
First available in Project Euclid: 15 November 2019

zbMATH: 07198794
MathSciNet: MR4061307
Digital Object Identifier: 10.12775/TMNA.2019.077

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 2A • 2019
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