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

The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (phi(x'))' = f(1)(t, x, x') + f(2)(t, x, x')F(1)x + f(3)(t, x, x') F(2)x,alpha(x) = 0, beta(x) = 0, where f(j) satisfy local Caratheodory conditions on some [0, T] x D-j subset of R-2, f(j) are either regular or have singularities in their phase variables (j = 1, 2, 3), F-i : C-1[0, T] -> C-0[0, T] (i = 1, 2), and alpha, beta : C-1[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. Copyright (c) 2006 Ravi P. Agarwal et al.