Positive solutions for nonlinear m-point Eigenvalue problems

In this paper, we are concerned with determining values of lambda, for which there exist positive solutions of the nonlinear eigenvalue problem [GRAPHICS] where a, b, c, d is an element of [0, infinity), xi(i) is an element of (0, 1), alpha(i), beta(i) is an element of [0 infinity) (for i is an element of {1, ..., m - 2}) are given constants, p, q is an element of C ([0, 1], (0, infinity)), h is an element of C ([0, 1], [0, infinity)), and f is an element of C ([0, infinity), [0, infinity)) satisfying some suitable conditions. Our proofs are based on Guo-Krasnoselskii fixed point theorem. (C) 2004 Elsevier Inc. All rights reserved.

Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.