Existence and global asymptotic behavior of positive solutions for nonlinear fractional Dirichlet problems on the half-line
type: Item
instance of: scholarly article
title: Existence and global asymptotic behavior of positive solutions for nonlinear fractional Dirichlet problems on the half-line
zbMATH Open document ID: 1474.34012
DOI: 10.1155/2014/537971
author: Imed Bachar
author: Habib Mâagli
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We are interested in the following fractional boundary value problem: \(D^\alpha u(t) + a \left(t\right) u^\sigma = 0\), \(t \in(0, \infty)\), \(\lim_{t \rightarrow 0} t^{2 - \alpha} u(t) = 0\), \(\lim_{t \rightarrow \infty} t^{1 - \alpha} u(t) = 0\), where \(1 < \alpha < 2\), \(\sigma \in(- 1,1)\), \(D^\alpha\) is the standard Riemann-Liouville fractional derivative, and \(a\) is a nonnegative continuous function on \((0, \infty)\) satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 7022577
Wikidata QID: Q59039256
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/537971
OpenAlex ID: W2095861037
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description: scientific article; zbMATH DE number 7022577