Abstract and Applied Analysis
Volume 2006 (2006), Article ID 96826, 30 pages
doi:10.1155/AAA/2006/96826
General existence principles for nonlocal boundary value problems with φ-Laplacian and their applications
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.
Abstract
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]×𝒟j⊂ℝ2, 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]→ℝ 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.