Positive solutions of singular dirichlet boundary value problems with sign-changing nonlinearities

By a new approach, we present a new existence result of positive solutions to the following Dirichlet boundary value problem, It is remarkable that the result of this paper is not obtained by employing the fixed-point theorems in cone and the method of the lower and upper functions. Our nonlinearity may change sign and be singular at t = 0, 1, χ = 0.