An existence theorem for singular boundary value problems with sign changing nonlinearities

In this paper we study the existence result of the singular boundary value problem − 1 p (pu) = f (t, u, pu), 0 < t < 1, lim t→0 + p(t)u (t) = 0 = u(1), Under the assumptions that the nonlinearity f may change sign and is singular at u = 0 and t = 1, we present sufficient conditions in Theorem 1.1 to ensure the existence of positive solutions. Our proof is based on the method of approximation and upper-lower solutions.