Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms

摘要

The singular two-point boundary value problem -u"(t) = h(t)f(u(t)), t is an element of (0, 1); U(O) = u(1) = 0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear problem, where h is allowed to be singular at both t = 0 and t = 1. Moreover, f : (-infinity, +infinity) -> (-infinity, +infinity) is a sign-changing function and not necessarily bounded from below. By computing the topological degree of an completely continuous field, the existence results of nontrivial solutions are established. (c) 2006 Elsevier Inc. All rights reserved.