Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities
Autor(a) principal: | |
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Data de Publicação: | 1998 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/27656 |
Resumo: | This paper is organized as follows: Introduction, In Section 2, we collect the notation and basic assumptions that we shall suppose fulfilled throughout this paper. Section 3 is devoted to second order nonlinear one-dimensional parabolic and (linearly) damped hyperbolic equations. We compare, in some sense, the nonlinearity g(x, u) with the Fuçik spectrum of the corresponding piecewise linear differential equations with homogeneous Dirichlet boundary conditions, and a resonance condition of Landesman-Lazer type with respect to the forcing term h(x, t). More specifically, we assume that (the asymptotic behavior of) u - ¹ g ( x , u) lies in a rectangle located in what we should call the Fucik -Landesman-Lazer "resolvent" set. In Section 4, we take up the case of second-order multi-dimensional equations, and we prove results on crossing at not necessarily simple (higher) eigenvalues. Finally, in Section 5 we indicate the conditions under which one can extend our results to higher-order multi-dimensional equations. |
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Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearitiesJumping NonlinearitiesTime-periodic SolutionsParabolic EquationsTelegraph EquationsFuçik SpectrumResonanceA Priori EstimatesDegree TheoryLP-theoryAnisotropic Sobolev-Slobodeckii SpacesThis paper is organized as follows: Introduction, In Section 2, we collect the notation and basic assumptions that we shall suppose fulfilled throughout this paper. Section 3 is devoted to second order nonlinear one-dimensional parabolic and (linearly) damped hyperbolic equations. We compare, in some sense, the nonlinearity g(x, u) with the Fuçik spectrum of the corresponding piecewise linear differential equations with homogeneous Dirichlet boundary conditions, and a resonance condition of Landesman-Lazer type with respect to the forcing term h(x, t). More specifically, we assume that (the asymptotic behavior of) u - ¹ g ( x , u) lies in a rectangle located in what we should call the Fucik -Landesman-Lazer "resolvent" set. In Section 4, we take up the case of second-order multi-dimensional equations, and we prove results on crossing at not necessarily simple (higher) eigenvalues. Finally, in Section 5 we indicate the conditions under which one can extend our results to higher-order multi-dimensional equations.Repositório da Universidade de LisboaGrossinho, Maria do RosárioNkashama, M. N.2023-04-24T10:52:57Z19981998-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/27656engGrossinho, Maria do Rosário and M.N. Nkashama .(1998). “Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities”. Nonlinear Analysis, Theory, Methods & Applications, Vol. 33, No. 2: pp. 187-210. (Search PDF in 2023).0362-546Xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-04-30T01:30:48Zoai:www.repository.utl.pt:10400.5/27656Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:50:25.973990Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
title |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
spellingShingle |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities Grossinho, Maria do Rosário Jumping Nonlinearities Time-periodic Solutions Parabolic Equations Telegraph Equations Fuçik Spectrum Resonance A Priori Estimates Degree Theory LP-theory Anisotropic Sobolev-Slobodeckii Spaces |
title_short |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
title_full |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
title_fullStr |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
title_full_unstemmed |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
title_sort |
Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities |
author |
Grossinho, Maria do Rosário |
author_facet |
Grossinho, Maria do Rosário Nkashama, M. N. |
author_role |
author |
author2 |
Nkashama, M. N. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Grossinho, Maria do Rosário Nkashama, M. N. |
dc.subject.por.fl_str_mv |
Jumping Nonlinearities Time-periodic Solutions Parabolic Equations Telegraph Equations Fuçik Spectrum Resonance A Priori Estimates Degree Theory LP-theory Anisotropic Sobolev-Slobodeckii Spaces |
topic |
Jumping Nonlinearities Time-periodic Solutions Parabolic Equations Telegraph Equations Fuçik Spectrum Resonance A Priori Estimates Degree Theory LP-theory Anisotropic Sobolev-Slobodeckii Spaces |
description |
This paper is organized as follows: Introduction, In Section 2, we collect the notation and basic assumptions that we shall suppose fulfilled throughout this paper. Section 3 is devoted to second order nonlinear one-dimensional parabolic and (linearly) damped hyperbolic equations. We compare, in some sense, the nonlinearity g(x, u) with the Fuçik spectrum of the corresponding piecewise linear differential equations with homogeneous Dirichlet boundary conditions, and a resonance condition of Landesman-Lazer type with respect to the forcing term h(x, t). More specifically, we assume that (the asymptotic behavior of) u - ¹ g ( x , u) lies in a rectangle located in what we should call the Fucik -Landesman-Lazer "resolvent" set. In Section 4, we take up the case of second-order multi-dimensional equations, and we prove results on crossing at not necessarily simple (higher) eigenvalues. Finally, in Section 5 we indicate the conditions under which one can extend our results to higher-order multi-dimensional equations. |
publishDate |
1998 |
dc.date.none.fl_str_mv |
1998 1998-01-01T00:00:00Z 2023-04-24T10:52:57Z |
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/10400.5/27656 |
url |
http://hdl.handle.net/10400.5/27656 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Grossinho, Maria do Rosário and M.N. Nkashama .(1998). “Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities”. Nonlinear Analysis, Theory, Methods & Applications, Vol. 33, No. 2: pp. 187-210. (Search PDF in 2023). 0362-546X |
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.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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