Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.21/676
Título: Solutions of second-order and fourth-order ODEs on the half-line
Autor: Enguiça, Ricardo Roque
Gavioli, Andrea
Sanchez, Luis
Palavras-chave: Second order
Fourth order
Non-autonomous equation
Variational methods
Unbounded intervals
Positive solution
Data: 1-Nov-2010
Editora: Pergamon-Elsevier Science LTD
Citação: Enguiça R, Gavioli A, Sanchez L. Solutions of second-order and fourth-order ODEs on the half-line.Nonlinear Analysis-Theory Methods & Applications. 2010; 73 (9): 2968-2979.
Relatório da Série N.º: 9
Resumo: We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.
Peer review: yes
URI: http://hdl.handle.net/10400.21/676
ISSN: 0362-546X
Aparece nas colecções:ISEL - Matemática - Artigos

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