EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN

Let Q : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img03.JPG" alt="http:/fbpe/img/proy/v27n2/img03.JPG">be a symmetric and positive semi-definite linear operator and f j : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img04.JPG...

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Autores principales:	HIDALGO,RUBÉN, GODOY,MAURICIO
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2008
Materias:	Graphs Partial difference equations Nonlinear elliptic equations Laplacian
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000200004
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spelling	oai:scielo:S0716-091720080002000042009-03-05EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN HIDALGO,RUBÉNGODOY,MAURICIO Graphs Partial difference equations Nonlinear elliptic equations Laplacian Let Q : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img03.JPG" alt="http:/fbpe/img/proy/v27n2/img03.JPG">be a symmetric and positive semi-definite linear operator and f j : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img04.JPG" alt="http:/fbpe/img/proy/v27n2/img04.JPG">(j = 1, 2, ...) be real functions so that, f j(0) = 0 and, for every x = (x1, x2, ....) <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img05.JPG" alt="http:/fbpe/img/proy/v27n2/img05.JPG"><img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">, it holds that f (x) := (f1(x1), f2(x2), ...) <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img05.JPG" alt="http:/fbpe/img/proy/v27n2/img05.JPG"><img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">. Sufficient conditions for the existence of non-trivial solutions to the semilinear problem Qx = f (x) are provided. Moreover, if G is a group of orthogonal linear automorphisms of <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">which commute with Q, then such sufficient conditions ensure the existence of non-trivial solutions which are invariant under G. As a consequence, sufficient conditions to ensure solutions of nonlinear partial difference equations on finite degree graphs with vertex set being either finite or infinitely countable are obtained. We consider adaptations to graphs of both Matukuma type equations and Helmholtz equations and study the existence of their solutions.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.27 n.2 20082008-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000200004en10.4067/S0716-09172008000200004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Graphs Partial difference equations Nonlinear elliptic equations Laplacian
spellingShingle	Graphs Partial difference equations Nonlinear elliptic equations Laplacian HIDALGO,RUBÉN GODOY,MAURICIO EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN
description	Let Q : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img03.JPG" alt="http:/fbpe/img/proy/v27n2/img03.JPG">be a symmetric and positive semi-definite linear operator and f j : <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img04.JPG" alt="http:/fbpe/img/proy/v27n2/img04.JPG">(j = 1, 2, ...) be real functions so that, f j(0) = 0 and, for every x = (x1, x2, ....) <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img05.JPG" alt="http:/fbpe/img/proy/v27n2/img05.JPG"><img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">, it holds that f (x) := (f1(x1), f2(x2), ...) <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img05.JPG" alt="http:/fbpe/img/proy/v27n2/img05.JPG"><img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">. Sufficient conditions for the existence of non-trivial solutions to the semilinear problem Qx = f (x) are provided. Moreover, if G is a group of orthogonal linear automorphisms of <img border=0 width=32 height=32 src="http:/fbpe/img/proy/v27n2/img02.JPG" alt="http:/fbpe/img/proy/v27n2/img02.JPG">which commute with Q, then such sufficient conditions ensure the existence of non-trivial solutions which are invariant under G. As a consequence, sufficient conditions to ensure solutions of nonlinear partial difference equations on finite degree graphs with vertex set being either finite or infinitely countable are obtained. We consider adaptations to graphs of both Matukuma type equations and Helmholtz equations and study the existence of their solutions.
author	HIDALGO,RUBÉN GODOY,MAURICIO
author_facet	HIDALGO,RUBÉN GODOY,MAURICIO
author_sort	HIDALGO,RUBÉN
title	EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN
title_short	EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN
title_full	EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN
title_fullStr	EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN
title_full_unstemmed	EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN
title_sort	existence of solutions of semilinear systems in
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2008
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000200004
work_keys_str_mv	AT hidalgoruben existenceofsolutionsofsemilinearsystemsin AT godoymauricio existenceofsolutionsofsemilinearsystemsin
_version_	1718439758395342848

EXISTENCE OF SOLUTIONS OF SEMILINEAR SYSTEMS IN

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