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=0t=0 and t=1t=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.