Strictly positive solutions for one dimensional nonlinear elliptic problems

Abstract

We study the existence and nonexistence of strictly positive solutions for the elliptic problems -- in a bounded open interval, with zero boundary conditions, where -- is a strongly uniformly elliptic differential operator, --, and -- is a function that changes sign. We also characterize the set of values-- for which the problem admits a solution, and in addition an existence result for other nonlinearities is presented.