Liouville type theorems for integral equations and integral systems
type: Item
instance of: scholarly article
title: Liouville type theorems for integral equations and integral systems
zbMATH Open document ID: 1262.45004
author: Xiaohui Yu
published in: Calculus of Variations and Partial Differential Equations
publication date: 2013-02-01T00:00:00Z
review text: The author establishes some Liouville type theorems for positive solutions of integral equations and integral systems in \(\mathbb R^N\) such as \[ u(x) = \int\limits_{\mathbb R^N} \frac{1}{|x-y|^{N-\alpha}} f(u(y)) dy, \, x \in \mathbb R^N, \] and \[ \begin{aligned} u(x) = \int\limits_{\mathbb R^N} \frac{1}{|x-y|^{N-\alpha}} f(u(y), v(y)) dy, \, x \in \mathbb R^N,\\ v(x) = \int\limits_{R^N} \frac{1}{|x-y|^{N-\alpha}} g(u(y), v(y)) dy, \, x \in \mathbb R^N, \end{aligned} \] where \(N \geq 2\), \(0 < \alpha < N\). The method of moving planes is used as the main technique.
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45M20
zbMATH DE Number: 6133429
zbMATH Keywords: Liouville type theorems
zbMATH Keywords: singular nonlinear integral equations
zbMATH Keywords: positive solution
zbMATH Keywords: method of moving planes
reviewed by: Ilia V. Boikov
MaRDI profile type: Publication
full work available at URL: s00526-011-0474-z
OpenAlex ID: W2068013636
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DOI: 10.1007/S00526-011-0474-Z
description: scientific article; zbMATH DE number 6133429