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Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian
Journal
Communications in Contemporary Mathematics
ISSN
1793-6683
Date Issued
2018-05-01
Author(s)
Xia, Aliang
Abstract
<jats:p>In this paper, we prove existence results of positive solutions for the following nonlinear elliptic problem with gradient terms: [Formula: see text] where [Formula: see text] denotes the fractional Laplacian and [Formula: see text] is a smooth bounded domain in [Formula: see text]. It shown that under some assumptions on [Formula: see text] and [Formula: see text], the problem has at least one positive solution [Formula: see text]. Our proof is based on the classical scaling method of Gidas and Spruck and topological degree theory.</jats:p>
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