On Hammerstein equations with natural growth conditions
type: Item
instance of: scholarly article
title: On Hammerstein equations with natural growth conditions
zbMATH Open document ID: 0942.45003
DOI: 10.4171/ZAA/902
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1999-12-20T00:00:00Z
full work available at URL: https://eudml.org/doc/48495
review text: Summary: We study a nonlinear Hammerstein integral equation by means of the direct variational method. Under certain ``natural'' growth conditions on the nonlinearity we show that the existence of a local minimum for the energy functional implies the solvability of the original equation. In these settings the energy functional may be non-smooth on its domain and, moreover, operators in data may be non-compact. Some solvability and nontrivial solvability results for the original equation are given.
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 1356399
zbMATH Keywords: natural growth conditions
zbMATH Keywords: nonlinear Hammerstein integral equation
zbMATH Keywords: energy functional
zbMATH Keywords: non-smooth functionals
zbMATH Keywords: direct variational method
zbMATH Keywords: nontrivial solvability
author: Vitaly Moroz
author: Peter P. Zabreĭko
MaRDI profile type: Publication
cites work: Q4860444
cites work: Euler equations involving nonlinearities without growth conditions
cites work: Zur Theorie der nichtlinearen Integralgleichungen, Integralgleichungssysteme und allgemeinen Funktionalgleichungen
cites work: SCALES OF BANACH SPACES
cites work: A variant of the mountain pass theorem and its application to Hammerstein integral equations
cites work: Completely continuous scalars and variational methods
cites work: Q3997570
cites work: Q3234774
description: scientific article; zbMATH DE number 1356399