POSITIVE SOLUTIONS OF A NONLINEAR STURM-LIOUVILLE BOUNDARY-VALUE PROBLEM

We establish the existence of positive solutions of the Sturm-Liouville problem - (p(s, u)u')' = (q) over cap (s)u(p)h(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) over cap 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.