Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 5707623, 8 pages
https://doi.org/10.1155/2017/5707623
Research Article

Monotone Iterative Technique for a Class of Slanted Cantilever Beam Equations

Department of Mathematics, Shanxi Normal University, Linfen 041000, China

Correspondence should be addressed to Qiang Li

Received 19 August 2017; Revised 1 December 2017; Accepted 13 December 2017; Published 31 December 2017

Academic Editor: Dan Simon

Copyright © 2017 Mei Wei and Qiang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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: ,  ,   where 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.