New existence and uniqueness results for an elastic beam equation with nonlinear boundary conditions

Boundary value problems

Chengbo Zhai¹  Shunyong Li² 

[1] School of Computer and Information Technology, Shanxi University, Taiyuan, P.R. China;School of Mathematical Sciences, Shanxi University, Taiyuan, P.R. China

关键词: existence and uniqueness;    monotone positive solution;    elastic beam equation;    fixed point theorem for mixed monotone operators;    34B18;    34B15;   

DOI  :  10.1186/s13661-015-0365-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we study the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions, and some sufficient conditions which guarantee the existence of unique monotone positive solution are established. The methods employed are two fixed point theorems for mixed monotone operators with perturbation. Our results can not only guarantee the existence of unique monotone positive solution, but also be applied to construct an iterative scheme for approximating it. Two examples are given to illustrate our main results.

【 授权许可】

CC BY