Abstract and Applied Analysis
Volume 2006 (2006), Article ID 96826, 30 pages

General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications

Ravi P. Agarwal,1 Donal O'Regan,2 and Svatoslav Staněk3

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, Florida, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland
3Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc 779 00, Czech Republic

Received 1 April 2005; Accepted 12 May 2005

Copyright © 2006 Ravi P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (φ(x))=f1(t,x,x)+f2(t,x,x)F1x+f3(t,x,x)F2x,α(x)=0, β(x)=0, where fj satisfy local Carathéodory conditions on some [0,T]×𝒟j2, fj are either regular or have singularities in their phase variables (j=1,2,3), Fi:C1[0,T]C0[0,T](i=1,2), and α,β:C1[0,T] are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.