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On the solvability of some fourth-order equations with functional boundary conditions

Pages: 564 - 573, Issue Special, September 2009

 Abstract        Full Text (145.9K)              

Feliz Minhós - Departamento de Matemática. Universidade de Évora, Centro de Investigação em Matemática e Aplicaçoes da U.E. (CIMA-UE), Rua Romão Ramalho, 59. 7000-671 Évora, Portugal (email)
João Fialho - Centro de Investigação em Matemática e Aplicações da U.E. (CIMA-CE), Rua Romão Ramalho 59, 7000-671 Évora, Portugal (email)

Abstract: In this paper it is considered a fourth order problem composed of a fully nonlinear differential equation and functional boundary conditions satisfying some monotone conditions.This functional dependence on $u,u^' $ and $u^{''}$and generalizes several types of boundary conditions such as Sturm-Liouville, multipoint, maximum and/or minimum arguments, or nonlocal. The main theorem is an existence and location result as it provides not only the existence, but also some qualitative information about the solution.

Keywords:  Fourth order functional problems, Nagumo-type condition, lower and upper solutions, beam equation, human spine continuous model
Mathematics Subject Classification:  Primary: 34B10, 34B15 ; Secondary: 34L30

Received: July 2008;      Revised: February 2009;      Published: September 2009.