- Open Access
Nonlocal boundary value problems
© Franco et al; licensee Springer. 2012
Received: 13 April 2011
Accepted: 24 February 2012
Published: 24 February 2012
In the last decades, nonlocal boundary value problems have become a rapidly growing area of research. The study of this type of problems is driven not only by a theoretical interest, but also by the fact that several phenomena in engineering, physics and life sciences can be modelled in this way. For example, problems with feedback controls such as the steady-states of a thermostat, where a controller at one of its ends adds or removes heat, depending upon the temperature registered in another point, can be interpreted with a second-order ordinary differential equation subject to a three-point boundary condition.
This volume contains a variety of contributions within this area of research. The first article, by Alberto Cabada, is an invited review on the applications of the method of upper and lower solutions to boundary value problems with nonlinear boundary data. The following articles deal with boundary value problems with nonlocal conditions for ordinary, discrete, impulsive, neutral, parabolic, fractional and time scales equations. The last two papers deal with problems where the nonlocality occurs in the equation, rather than in the boundary conditions.
In the contributions, existence, nonexistence, multiplicity, asymptotic behavior, and approx-imation of solutions are considered by using several methods as fixed point theorems, fixed point index, variational methods, iterative techniques, bifurcation theory, and lower and upper solutions.
We would like to thank the authors for their contributions and the anonymous referees for their professional support.
We wish to thank the staff of the Editorial Office of Boundary Value Problems, for their help throughout the realization of this volume.
It is our great pleasure to thank Professor Ravi P. Agarwal, Editor-in-Chief of Boundary Value Problems, for giving us the opportunity to prepare this volume.
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.