Positive solutions for some competitive fractional systems in bounded domains
type: Item
instance of: scholarly article
title: Positive solutions for some competitive fractional systems in bounded domains
zbMATH Open document ID: 1302.35397
DOI: 10.1155/2013/140130
author: Imed Bachar
author: Habib Mâagli
author: Noureddine Zeddini
published in: Journal of Function Spaces and Applications
publication date: 2013-05-29T00:00:00Z
review text: Summary: Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system \((-\Delta_{|D})^{\alpha/2}u + p(x)u^\sigma v^r = 0\), \((-\Delta_{|D})^{\alpha/2}v + q(x)u^sv^\beta = 0\) in a bounded \(C^{1,1}\)-domain \(D\) in \(\mathbb R^n(n \geq 3)\), subject to some Dirichlet conditions, where \(0 < \alpha < 2, \sigma, \beta \geq 1, s, r \geq 0\). The potential functions \(p, q\) are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions \(K_\alpha(D)\).
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6167891
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/140130
OpenAlex ID: W2121072673
Wikidata QID: Q59013534
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description: scientific article; zbMATH DE number 6167891