Variational method with application to convolution equations
type: Item
instance of: scholarly article
title: Variational method with application to convolution equations
zbMATH Open document ID: 0820.45004
published in: Journal of Integral Equations and Applications
publication date: 1995-09-21T00:00:00Z
review text: The author considers the problem of solvability for the nonlinear integral equation \(k* u^ 2= | u|\). Here \(u\in L^ 3(\mathbb{R})\), and \(k\in L^{3/2}(\mathbb{R})\) satisfies the conditions: \(k(x)\geq 0\), \(k(x)= k(- x)\) and \(k\) is symmetrically decreasing. The investigation is based on some variational method and results due to \textit{A. Szulkin} [Ann. Inst. Henri Poincaré Anal. Non Linéaire 5, No. 2, 119-139 (1988; Zbl 0661.58009)].
Mathematics Subject Classification ID: 45G05
zbMATH DE Number: 739389
zbMATH Keywords: convolution equations
zbMATH Keywords: nonlinear integral equation
zbMATH Keywords: variational method
author: Daniel Goeleven
reviewed by: N. Karapetiants
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075818
OpenAlex ID: W2056021663
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DOI: 10.1216/JIEA/1181075818
description: scientific article; zbMATH DE number 739389