EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF FOURTH ORDER BOUNDARY VALUE PROBLEMS

Abstract

We prove the existence of multiple solutions for the fourth order differential equation $u^{(4)}(t)=\lambda h\left(t, u(t), u''(t)\right)$ under certain nonhomogeneous boundary conditions. Here $\lambda>0$, and $h$ is assumed to be a nonnegative continuous function satisfying appropriate constraints. The proof involves transforming the fourth order problem into a system of two second order differential equations, and then using the Guo-Krasnosel'skii Fixed Point Theorem to establish the existence of at least three solutions.