General existence principles for nonlocal boundary value problems with φ-Laplacian and their applicationsReport as inadecuate




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



Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901-6975, USA

Department of Mathematics, National University of Ireland, Galway, Ireland

Department 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 usedfor a large class of nonlocal boundary value problems of the form φx′′=f1t,x,x′+f2t,x,x′F1x+f3t,x,x′F2x,αx=0, βx=0, where fj satisfy local Carathéodoryconditions on some 0,T×and#x1D49F;j⊂ℝ2, fj are either regular or have singularities in their phase variables j=1,2,3, Fi:C10,T→C00,Ti=1,2, and α,β:C10,T→ℝ are continuous. The proofsare based on the Leray-Schauder degree theory and useregularization and sequential techniques. Applications of generalexistence principles to singular BVPs are given.





Author: Ravi P. Agarwal, Donal O-Regan, and Svatoslav Stanek

Source: https://www.hindawi.com/



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