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

The singular two-point boundary value problem −u (t) = h(t)f u(t) , t∈ (0, 1); u(0) = 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 : (−∞,+∞) → (−∞,+∞) 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. © 2006 Elsevier Inc. All rights reserved