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

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2009, 2009(Special): 564-573. doi: 10.3934/proc.2009.2009.564

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

1.	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
2.	Centro de Investigação em Matemática e Aplicações da U.E. (CIMA-CE), Rua Romão Ramalho 59, 7000-671 Évora, Portugal

Received July 2008 Revised February 2009 Published September 2009

Abstract
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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: lower and upper solutions, human spine continuous model, Fourth order functional problems, beam equation, Nagumo-type condition.

Mathematics Subject Classification: Primary: 34B10, 34B15 ; Secondary: 34L30.

Citation: Feliz Minhós, João Fialho. On the solvability of some fourth-order equations with functional boundary conditions. Conference Publications, 2009, 2009 (Special) : 564-573. doi: 10.3934/proc.2009.2009.564

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