On one-dimensional superlinear indefinite problems involving the φ-Laplacian

Let Omega := (a, b) subset of R, m is an element of L-1 (Omega) and phi : R -> R be an odd increasing homeomorphism. We consider the existence of positive solutions for problems of the form {-phi(u')' = m(x) f(u) in Omega, u = 0 on partial derivative Omega, where f : [0, infinity) -> [0, infinity) is a continuous function which is, roughly speaking, superlinear with respect to phi. Our approach combines the Guo-Krasnoselskii fixed-point theorem with some estimates on related nonlinear problems. We mention that our results are new even in the case m >= 0.