On quasilinear elliptic equations in ℝN

In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −Δu=h(x)uq in ℝN, where 0<q<1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super sol...

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Main Authors: C. O. Alves, J. V. Concalves, L. A. Maia
Format: Article
Language:English
Published: Wiley 1996-01-01
Series:Abstract and Applied Analysis
Subjects:
Online Access:http://dx.doi.org/10.1155/S108533759600022X
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author C. O. Alves
J. V. Concalves
L. A. Maia
author_facet C. O. Alves
J. V. Concalves
L. A. Maia
author_sort C. O. Alves
collection DOAJ
description In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −Δu=h(x)uq in ℝN, where 0<q<1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.
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institution Kabale University
issn 1085-3375
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publishDate 1996-01-01
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series Abstract and Applied Analysis
spelling doaj-art-0cb45a77c4884838b85dcd6cfc0c1a892025-02-03T01:27:10ZengWileyAbstract and Applied Analysis1085-33751996-01-011440741510.1155/S108533759600022XOn quasilinear elliptic equations in ℝNC. O. Alves0J. V. Concalves1L. A. Maia2Departamento de Matemática, Universidade Federal da Paraiba, Campina Grande-(PB), 58100-240 -, BrazilDepartamento de Matemática, Universidade de Brasília, Brasilia 70.910-900, DF, BrazilDepartamento de Matemática, Universidade de Brasília, Brasilia 70.910-900, DF, BrazilIn this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −Δu=h(x)uq in ℝN, where 0<q<1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.http://dx.doi.org/10.1155/S108533759600022XQuasilinear elliptic equationp-Laplacianvariational method.
spellingShingle C. O. Alves
J. V. Concalves
L. A. Maia
On quasilinear elliptic equations in ℝN
Abstract and Applied Analysis
Quasilinear elliptic equation
p-Laplacian
variational method.
title On quasilinear elliptic equations in ℝN
title_full On quasilinear elliptic equations in ℝN
title_fullStr On quasilinear elliptic equations in ℝN
title_full_unstemmed On quasilinear elliptic equations in ℝN
title_short On quasilinear elliptic equations in ℝN
title_sort on quasilinear elliptic equations in rn
topic Quasilinear elliptic equation
p-Laplacian
variational method.
url http://dx.doi.org/10.1155/S108533759600022X
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AT jvconcalves onquasilinearellipticequationsinrn
AT lamaia onquasilinearellipticequationsinrn