Multiple Positive Solutions for a Fourth-order Boundary Value Problem

Abstract

In this paper, we discuss the existence of multiple positive solutions for the fourth-order boundary value problemu^(4)(t) = f(t,u(t)), 0 < t < 1,u(0) = u(1) = u''(0) = u''(1) = 0,where f : [0, 1] × [0,∞) → [0,∞) is continuous. Existence theorems are established via the theory of fixed point index in cones.

Keywords

• multiple positive solutions
• nonlinear ODE
• theory of fixed point index in cones.