EIGENVALUE OF FOURTH-ORDER STURM-LIOUVILLE BOUNDARY VALUE PROBLEM WITH BENDING TERM

Abstract

In this paper, we consider the existence of positive solutions for the singular fourth-order Sturm-Liouville boundary value problem. By choosing proper cone and creating an integral operator, we, using fixed point index theory, in the case without any monotone-type assumption on f obtain the positive solution of the singular Sturm-Liouville boundary value problem when lambda is in an explicit interval. Our results essentially improve, generalize and unify many well-known results.