Eigenvalues of an Operator Homogeneous at the Infinity

Eigenvalues of an Operator Homogeneous at the Infinity

In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study thesolvability of the problemA(u) := −div(A(x,∇u)) = f(x, u) + h in...

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Main Authors: Mohammed Filali, Belhadj Karim, Omar Chakrone, Aomar Anane
Format: Article
Language:English
Published: Sociedade Brasileira de Matemática 2010-07-01
Series:Boletim da Sociedade Paranaense de Matemática
Subjects:
Operator homogeneous at infinity
Eigenvalues
Boundary Value problem.
Online Access:http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10815/5837
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spelling doaj-b610d54d3ac14ae7bf99ab1a4230b7d72020-11-25T01:35:15ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882010-07-012815165Eigenvalues of an Operator Homogeneous at the InfinityMohammed FilaliBelhadj KarimOmar ChakroneAomar AnaneIn this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study thesolvability of the problemA(u) := −div(A(x,∇u)) = f(x, u) + h in Ω,u = 0 on ∂Ω,as well as the spectrum ofG_0'(u) = λm|u|^{p−2}u in Ω,u = 0 on ∂Ω.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10815/5837Operator homogeneous at infinityEigenvaluesBoundary Value problem.
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed Filali
Belhadj Karim
Omar Chakrone
Aomar Anane
spellingShingle Mohammed Filali
Belhadj Karim
Omar Chakrone
Aomar Anane
Eigenvalues of an Operator Homogeneous at the Infinity
Boletim da Sociedade Paranaense de Matemática
Operator homogeneous at infinity
Eigenvalues
Boundary Value problem.
author_facet Mohammed Filali
Belhadj Karim
Omar Chakrone
Aomar Anane
author_sort Mohammed Filali
title Eigenvalues of an Operator Homogeneous at the Infinity
title_short Eigenvalues of an Operator Homogeneous at the Infinity
title_full Eigenvalues of an Operator Homogeneous at the Infinity
title_fullStr Eigenvalues of an Operator Homogeneous at the Infinity
title_full_unstemmed Eigenvalues of an Operator Homogeneous at the Infinity
title_sort eigenvalues of an operator homogeneous at the infinity
publisher Sociedade Brasileira de Matemática
series Boletim da Sociedade Paranaense de Matemática
issn 0037-8712
2175-1188
publishDate 2010-07-01
description In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study thesolvability of the problemA(u) := −div(A(x,∇u)) = f(x, u) + h in Ω,u = 0 on ∂Ω,as well as the spectrum ofG_0'(u) = λm|u|^{p−2}u in Ω,u = 0 on ∂Ω.
topic Operator homogeneous at infinity
Eigenvalues
Boundary Value problem.
url http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10815/5837
work_keys_str_mv AT mohammedfilali eigenvaluesofanoperatorhomogeneousattheinfinity
AT belhadjkarim eigenvaluesofanoperatorhomogeneousattheinfinity
AT omarchakrone eigenvaluesofanoperatorhomogeneousattheinfinity
AT aomaranane eigenvaluesofanoperatorhomogeneousattheinfinity
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