Monotone Iterative Technique for a Class of Slanted Cantilever Beam Equations

Abstract

In this paper, we deal with the existence and uniqueness of the solutions of two-point boundary value problem of fourth-order ordinary differential equation: u4(t)=f(t,u(t),u′(t)),  t∈[0,1],  u(0)=u′(0)=u′′(1)=u′′′(1)=0, where f:[0,1]×R2→R is a continuous function. The problem describes the static deformation of an elastic beam whose left end-point is fixed and right is freed, which is called slanted cantilever beam. Under some weaker assumptions, we establish a new maximum principle by the perturbation of positive operator and construct the monotone iterative sequence of the lower and upper solutions, and, based on this, we obtain the existence and uniqueness results for the slanted cantilever beam.