Existence and uniqueness of positive solution for a fractional Dirichlet problem with combined nonlinear effects in bounded domains
type: Item
instance of: scholarly article
title: Existence and uniqueness of positive solution for a fractional Dirichlet problem with combined nonlinear effects in bounded domains
zbMATH Open document ID: 1293.35356
DOI: 10.1155/2013/295480
author: Imed Bachar
author: Habib Mâagli
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We prove the existence and uniqueness of a positive continuous solution to the following singular semilinear fractional Dirichlet problem \((-\Delta)^{\alpha/2}u=a_1(x)u^{\sigma_1}+a_2(x)u^{\sigma_2}\) in \(D\), \(\lim_{x\to z\in\partial D}(\delta(x))^{1-(\alpha/2)}u(x)=0\), where \(0<\alpha<2\), \(\sigma_1\), \(\sigma_2 \in (-1,1)\), \(D\) is a bounded \(C^{1,1}\)-domain in \(\mathbb R^n\), \(n\geq 2\) and \(\delta(x)\) denotes the Euclidian distance from \(x\) to the boundary of \(D\). The nonnegative weight functions \(a_1\), \(a_2\) are required to satisfy certain hypotheses related to the Karamata class. We also investigate the global behavior of such solutions.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 6306629
zbMATH Keywords: fractional Dirichlet problem
zbMATH Keywords: positive continuous solution
zbMATH Keywords: nonnegative weights
zbMATH Keywords: Karamata class
Wikidata QID: Q58915857
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/295480
OpenAlex ID: W2127223125
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description: scientific article; zbMATH DE number 6306629