Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.21/2229
Título: Positive solutions of fourth order problems with clamped beam boundary conditions
Autor: Cabada, Alberto
Enguiça, Ricardo Roque
Palavras-chave: Clamped Beam
Fourth Order Boundary Value Problem
Maximum Principles
Maximum Principles
Data: Jul-2011
Editora: Pergamon-Elsevier Science LTD
Citação: CABADA, Alberto; ENGUIÇA, Ricardo Roque - Positive solutions of fourth order problems with clamped beam boundary conditions. Nonlinear Analysis-Theory Methods & Applications. ISSN 0362-546X. Vol. 74, n.º 10 (2011) p. 3112-3122.
Resumo: n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.
Peer review: yes
URI: http://hdl.handle.net/10400.21/2229
ISSN: 0362-546X
Aparece nas colecções:ISEL - Matemática - Artigos

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