CRITICAL POINT THEOREMS AND APPLICATIONS

CRITICAL POINT THEOREMS AND APPLICATIONS

We Consider the nonlinear Dirichlet problem: <IMG SRC="http:/fbpe/img/proy/v21n3/img04-01.gif" WIDTH=350 HEIGHT=56> where . omega <FONT FACE=Symbol>Î</FONT> R N is a bounded open domain, F : omega chi R -> R is a carath´eodory function and DuF(x; u) is the partial deri...

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Autores principales: BOUKHRISSE,HAFIDA, MOUSSAOUI,MIMOUN
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2002
Materias:
Critical point theory
convexity conditions
Elliptic semilinear problem
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172002000300004
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spelling oai:scielo:S0716-091720020003000042003-03-31CRITICAL POINT THEOREMS AND APPLICATIONSBOUKHRISSE,HAFIDAMOUSSAOUI,MIMOUN Critical point theory convexity conditions Elliptic semilinear problem We Consider the nonlinear Dirichlet problem: <IMG SRC="http:/fbpe/img/proy/v21n3/img04-01.gif" WIDTH=350 HEIGHT=56> where . omega <FONT FACE=Symbol>Î</FONT> R N is a bounded open domain, F : omega chi R -> R is a carath´eodory function and DuF(x; u) is the partial derivative of F. We are interested in the resolution of problem (1) when F is concave. Our tool is absolutely variational. Therefore, we state and prove a critical point theorem which generalizes many other results in the literature and leads to the resolution of problem (1). Our theorem allows us to express our assumptions on the nonlinearity in terms of F and not of <FONT FACE=Symbol>Ñ</FONT>F. Also, we note that our theorem doesn’t necessitate the verification of the famous compactness condition introduced by Palais-Smale or any of its variantsinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.21 n.3 20022002-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172002000300004en10.4067/S0716-09172002000300004
institution Scielo Chile
collection Scielo Chile
language English
topic Critical point theory
convexity conditions
Elliptic semilinear problem
spellingShingle Critical point theory
convexity conditions
Elliptic semilinear problem
BOUKHRISSE,HAFIDA
MOUSSAOUI,MIMOUN
CRITICAL POINT THEOREMS AND APPLICATIONS
description We Consider the nonlinear Dirichlet problem: <IMG SRC="http:/fbpe/img/proy/v21n3/img04-01.gif" WIDTH=350 HEIGHT=56> where . omega <FONT FACE=Symbol>Î</FONT> R N is a bounded open domain, F : omega chi R -> R is a carath´eodory function and DuF(x; u) is the partial derivative of F. We are interested in the resolution of problem (1) when F is concave. Our tool is absolutely variational. Therefore, we state and prove a critical point theorem which generalizes many other results in the literature and leads to the resolution of problem (1). Our theorem allows us to express our assumptions on the nonlinearity in terms of F and not of <FONT FACE=Symbol>Ñ</FONT>F. Also, we note that our theorem doesn’t necessitate the verification of the famous compactness condition introduced by Palais-Smale or any of its variants
author BOUKHRISSE,HAFIDA
MOUSSAOUI,MIMOUN
author_facet BOUKHRISSE,HAFIDA
MOUSSAOUI,MIMOUN
author_sort BOUKHRISSE,HAFIDA
title CRITICAL POINT THEOREMS AND APPLICATIONS
title_short CRITICAL POINT THEOREMS AND APPLICATIONS
title_full CRITICAL POINT THEOREMS AND APPLICATIONS
title_fullStr CRITICAL POINT THEOREMS AND APPLICATIONS
title_full_unstemmed CRITICAL POINT THEOREMS AND APPLICATIONS
title_sort critical point theorems and applications
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2002
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172002000300004
work_keys_str_mv AT boukhrissehafida criticalpointtheoremsandapplications
AT moussaouimimoun criticalpointtheoremsandapplications
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