Two nontrivial solutions of a class of elliptic equations with singular term

Bibliographic Details
Main Author: Chen, J.
Publication Date: 2011
Other Authors: Murillo, K., Rocha, E. M.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/41618
Summary: We consider the existence of nontrivial solutions of the equation -Δu -λ/|x|2 u = |u|2*-2u + μ|x| α-2u + f(x)|u|γ, x ∈Ω\ -0}, u∈ H 01 (Ω); where 0 ∈ Ω is a smooth bounded domain in ℝN (N ≥ 3). By variational methods and Nehari set techniques, we show that this equation has at least two nontrivial solutions in H0 1 (Ω), under some additional hypotheses on λ > 0, μ > 0, α > 0, 0 ≤ γ < 1 and f ∈ L∞(Ω), which may be sign-changing. If f > 0 then the solutions are positive.
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spelling Two nontrivial solutions of a class of elliptic equations with singular termInhomogeneous Laplacian equationSingular termTwo solutionsVariational methodsWe consider the existence of nontrivial solutions of the equation -Δu -λ/|x|2 u = |u|2*-2u + μ|x| α-2u + f(x)|u|γ, x ∈Ω\ -0}, u∈ H 01 (Ω); where 0 ∈ Ω is a smooth bounded domain in ℝN (N ≥ 3). By variational methods and Nehari set techniques, we show that this equation has at least two nontrivial solutions in H0 1 (Ω), under some additional hypotheses on λ > 0, μ > 0, α > 0, 0 ≤ γ < 1 and f ∈ L∞(Ω), which may be sign-changing. If f > 0 then the solutions are positive.AIMS2024-04-19T08:45:45Z2011-01-01T00:00:00Z2011info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/41618eng1078-094710.3934/proc.2011.2011.272Chen, J.Murillo, K.Rocha, E. M.info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:55:02Zoai:ria.ua.pt:10773/41618Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:24:08.023884Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Two nontrivial solutions of a class of elliptic equations with singular term
title Two nontrivial solutions of a class of elliptic equations with singular term
spellingShingle Two nontrivial solutions of a class of elliptic equations with singular term
Chen, J.
Inhomogeneous Laplacian equation
Singular term
Two solutions
Variational methods
title_short Two nontrivial solutions of a class of elliptic equations with singular term
title_full Two nontrivial solutions of a class of elliptic equations with singular term
title_fullStr Two nontrivial solutions of a class of elliptic equations with singular term
title_full_unstemmed Two nontrivial solutions of a class of elliptic equations with singular term
title_sort Two nontrivial solutions of a class of elliptic equations with singular term
author Chen, J.
author_facet Chen, J.
Murillo, K.
Rocha, E. M.
author_role author
author2 Murillo, K.
Rocha, E. M.
author2_role author
author
dc.contributor.author.fl_str_mv Chen, J.
Murillo, K.
Rocha, E. M.
dc.subject.por.fl_str_mv Inhomogeneous Laplacian equation
Singular term
Two solutions
Variational methods
topic Inhomogeneous Laplacian equation
Singular term
Two solutions
Variational methods
description We consider the existence of nontrivial solutions of the equation -Δu -λ/|x|2 u = |u|2*-2u + μ|x| α-2u + f(x)|u|γ, x ∈Ω\ -0}, u∈ H 01 (Ω); where 0 ∈ Ω is a smooth bounded domain in ℝN (N ≥ 3). By variational methods and Nehari set techniques, we show that this equation has at least two nontrivial solutions in H0 1 (Ω), under some additional hypotheses on λ > 0, μ > 0, α > 0, 0 ≤ γ < 1 and f ∈ L∞(Ω), which may be sign-changing. If f > 0 then the solutions are positive.
publishDate 2011
dc.date.none.fl_str_mv 2011-01-01T00:00:00Z
2011
2024-04-19T08:45:45Z
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://hdl.handle.net/10773/41618
url http://hdl.handle.net/10773/41618
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1078-0947
10.3934/proc.2011.2011.272
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv AIMS
publisher.none.fl_str_mv AIMS
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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