Three weak solutions for nonlocal fractional Laplacian equations
type: Item
instance of: scholarly article
title: Three weak solutions for nonlocal fractional Laplacian equations
zbMATH Open document ID: 1474.35676
DOI: 10.1155/2014/809769
author: Dandan Yang
author: Chuanzhi Bai
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The existence of three weak solutions for the following nonlocal fractional equation \((- \Delta)^s u - \lambda u = \mu f(x, u)\) in \(\Omega, u = 0\) in \(\mathbb{R}^n \smallsetminus \Omega\), is investigated, where \(s \in(0,1)\) is fixed, \((- \Delta)^s\) is the fractional Laplace operator, \(\lambda\) and \(\mu\) are real parameters, \(\Omega\) is an open bounded subset of \(\mathbb{R}^n\), \(n > 2 s\), and the function \(f\) satisfies some regularity and natural growth conditions. The approach is based on a three-critical-point theorem for differential functionals.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 7023122
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/809769
OpenAlex ID: W2039237851
Wikidata QID: Q59041703
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description: scientific article; zbMATH DE number 7023122