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2011, 2011(Special): 209-218. doi: 10.3934/proc.2011.2011.209

Non ordered lower and upper solutions to fourth order problems with functional boundary conditions

Alberto Cabada 1, , João Fialho 2, and  Feliz Minhós 3,

1. 

University of Santiago de Compostela, Department of Mathematical Analysis, Santiago de Compostela, Galicia
2. 

Centro de Investigação em Matemática e Aplicações da U.E. (CIMA-CE), Rua Romão Ramalho 59, 7000-671 Évora
3. 

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

Received  July 2010 Revised  April 2011 Published  October 2011

In this paper, given $f : I \times (C(I))^2 \times \mathbb{R}^2 \leftarrow \mathbb{R}$ a $L^1$ Carathéodory function, it is considered the functional fourth order equation $u^(iv) (x) = f(x, u, u', u'' (x), u''' (x))$ together with the nonlinear functional boundary conditions $L_0(u, u', u'', u (a)) = 0 = L_1(u, u', u'', u' (a))$ $L_2(u, u', u'', u'' (a), u''' (a)) = 0 = L_3(u, u', u'', u'' (b}, u''' (b)):$ Here $L_i, i$ = 0; 1; 2; 3, are continuous functions satisfying some adequate monotonicity assumptions. It will be proved an existence and location result in presence of non ordered lower and upper solutions and without monotone assumptions on the right hand side of the equation.
Keywords: functional boundary value problems, Higher order problems, Nagumo condition, lower and upper solutions.
Mathematics Subject Classification: Primary: 34B15, 34K10; Secondary: 34B10, 34K45.
Citation: Alberto Cabada, João Fialho, Feliz Minhós. Non ordered lower and upper solutions to fourth order problems with functional boundary conditions. Conference Publications, 2011, 2011 (Special) : 209-218. doi: 10.3934/proc.2011.2011.209
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