SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Higher order functional boundary value problems without monotone assumptions

João F Fialho13* and Feliz Minhós23

Author Affiliations

1 School of Mathematics, Physics and Technology, College of the Bahamas, Nassau, Bahamas

2 Department of Mathematics, School of Sciences and Technology, University of Évora, Évora, Portugal

3 Research Centre on Mathematics and Applications, University of Évora (CIMA-UE), Rua Romão Ramalho, 59, Évora, 7000-671, Portugal

For all author emails, please log on.

Boundary Value Problems 2013, 2013:81  doi:10.1186/1687-2770-2013-81

Published: 10 April 2013

Abstract

In this paper, given <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M1">View MathML</a> a <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M2">View MathML</a>-Carathéodory function, it is considered the functional higher order equation

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M3">View MathML</a>

together with the nonlinear functional boundary conditions, for <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M4">View MathML</a>

Here, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M6">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/81/mathml/M7">View MathML</a>, are continuous functions. It will be proved an existence and location result in presence of not necessarily ordered lower and upper solutions, without assuming any monotone properties on the boundary conditions and on the nonlinearity f.