Abstract

We establish the existence of positive solutions of the Sturm-Liouville problem ?(p(s, u)u′)′ = q̂(s)uph(s, u, u′) in(0, 1), u(0) = 0 = u(1),where p(s, u) = 1/(a(s) + cg(u)).We assume g and q}̂ to be non-negative, continuous functions, a(s) is a positive continuous function, c ≥ 0, p>1, and the function h is sub-quadratic with respect to u. We combine a priori estimates with a fixed-point result of Krasnosel'skii to obtain the existence of a positive solution. © 2009 Edinburgh Mathematical Society.