Nontrivial solution for Schrödinger-Poisson equations involving a fractional nonlocal operator via perturbation methods
type: Item
instance of: scholarly article
title: Nontrivial solution for Schrödinger-Poisson equations involving a fractional nonlocal operator via perturbation methods
zbMATH Open document ID: 1386.35433
author: Xiaojing Feng
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2016-10-14T00:00:00Z
review text: From the abstract: ''This paper focuses on the following Schrödinger-Poisson equations involving a fractional nonlocal operator \[ \begin{cases} -\Delta u + u + \phi u = f(x, u),\quad &\text{in }\mathbb{R}^3,\\ (-\Delta)^{\alpha/2}\phi = u^2, \quad&\text{in }\mathbb{R}^3, \\ \, \lim_{|x|\to\infty}\phi(x) = 0, \end{cases} \] where \(\alpha \in (1,2]\). Under certain assumptions, we obtain the existence of nontrivial solution of the above problem without compactness by using the methods of perturbation and the mountain pass theorem.''
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 6639267
zbMATH Keywords: Schrödinger-Poisson
zbMATH Keywords: perturbation methods
zbMATH Keywords: nontrivial solution
MaRDI profile type: Publication
full work available at URL: s00033-016-0667-6
OpenAlex ID: W2399460807
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DOI: 10.1007/S00033-016-0667-6
description: scientific article; zbMATH DE number 6639267