Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1186/1687-2770-2013-92 http://hdl.handle.net/11449/111584 |
Resumo: | We establish the existence of positive solution for the following class of degenerate quasilinear elliptic problem(P) {-Lu-ap + V(x)vertical bar x vertical bar(-ap*)vertical bar u vertical bar(p-2)u = f(u) in R-N, u > 0 in R-N; u is an element of D-a(1,p) (R-N)where -Lu-ap = -div(vertical bar x vertical bar(-ap)vertical bar del vertical bar(p-2)del u), 1 < N, -infinity < a < N-p/p, a <= e <= a + 1, d = 1 + a - e, and p* = p* (a, e) = Np/N-dp denote the Hardy-Sobolev's critical exponent, V is a bounded nonnegative vanishing potential and f has a subcritical growth at infinity. The technique used here is a truncation argument together with the variational approach. |
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Repositório Institucional da UNESP |
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Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentialsWe establish the existence of positive solution for the following class of degenerate quasilinear elliptic problem(P) {-Lu-ap + V(x)vertical bar x vertical bar(-ap*)vertical bar u vertical bar(p-2)u = f(u) in R-N, u > 0 in R-N; u is an element of D-a(1,p) (R-N)where -Lu-ap = -div(vertical bar x vertical bar(-ap)vertical bar del vertical bar(p-2)del u), 1 < N, -infinity < a < N-p/p, a <= e <= a + 1, d = 1 + a - e, and p* = p* (a, e) = Np/N-dp denote the Hardy-Sobolev's critical exponent, V is a bounded nonnegative vanishing potential and f has a subcritical growth at infinity. The technique used here is a truncation argument together with the variational approach.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Univ Estadual Paulista, BR-15054000 Sao Paulo, BrazilUniv Fed Juiz de Fora, BR-36036330 Juiz De Fora, MG, BrazilCtr Fed Educ Tecnol Minas Gerais, BR-35503822 Divinopolis, MG, BrazilUniv Estadual Paulista, BR-15054000 Sao Paulo, BrazilFAPEMIG: CEX-APQ 00025-11SpringerUniversidade Estadual Paulista (Unesp)Universidade Federal de Juiz de Fora (UFJF)Centro Federal de Educação Tecnológica (CEFET)Bastos, Waldemar D. [UNESP]Miyagaki, Olimpio H.Vieira, Ronei S.2014-12-03T13:08:47Z2014-12-03T13:08:47Z2013-04-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article16application/pdfhttp://dx.doi.org/10.1186/1687-2770-2013-92Boundary Value Problems. Cham: Springer International Publishing Ag, 16 p., 2013.1687-2770http://hdl.handle.net/11449/11158410.1186/1687-2770-2013-92WOS:000333981800001WOS000333981800001.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBoundary Value Problems1.1560,490info:eu-repo/semantics/openAccess2024-01-15T06:18:03Zoai:repositorio.unesp.br:11449/111584Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-01-15T06:18:03Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
title |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
spellingShingle |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials Bastos, Waldemar D. [UNESP] |
title_short |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
title_full |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
title_fullStr |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
title_full_unstemmed |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
title_sort |
Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials |
author |
Bastos, Waldemar D. [UNESP] |
author_facet |
Bastos, Waldemar D. [UNESP] Miyagaki, Olimpio H. Vieira, Ronei S. |
author_role |
author |
author2 |
Miyagaki, Olimpio H. Vieira, Ronei S. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Federal de Juiz de Fora (UFJF) Centro Federal de Educação Tecnológica (CEFET) |
dc.contributor.author.fl_str_mv |
Bastos, Waldemar D. [UNESP] Miyagaki, Olimpio H. Vieira, Ronei S. |
description |
We establish the existence of positive solution for the following class of degenerate quasilinear elliptic problem(P) {-Lu-ap + V(x)vertical bar x vertical bar(-ap*)vertical bar u vertical bar(p-2)u = f(u) in R-N, u > 0 in R-N; u is an element of D-a(1,p) (R-N)where -Lu-ap = -div(vertical bar x vertical bar(-ap)vertical bar del vertical bar(p-2)del u), 1 < N, -infinity < a < N-p/p, a <= e <= a + 1, d = 1 + a - e, and p* = p* (a, e) = Np/N-dp denote the Hardy-Sobolev's critical exponent, V is a bounded nonnegative vanishing potential and f has a subcritical growth at infinity. The technique used here is a truncation argument together with the variational approach. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-04-17 2014-12-03T13:08:47Z 2014-12-03T13:08:47Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1186/1687-2770-2013-92 Boundary Value Problems. Cham: Springer International Publishing Ag, 16 p., 2013. 1687-2770 http://hdl.handle.net/11449/111584 10.1186/1687-2770-2013-92 WOS:000333981800001 WOS000333981800001.pdf |
url |
http://dx.doi.org/10.1186/1687-2770-2013-92 http://hdl.handle.net/11449/111584 |
identifier_str_mv |
Boundary Value Problems. Cham: Springer International Publishing Ag, 16 p., 2013. 1687-2770 10.1186/1687-2770-2013-92 WOS:000333981800001 WOS000333981800001.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Boundary Value Problems 1.156 0,490 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
16 application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1797790297749454848 |