Lower and upper solutions method to the fully elastic cantilever beam equation with support

Advances in Difference Equations

article

Wei, Mei¹  Li, Yongxiang¹  Li, Gang² 

[1] Department of Mathematics, Northwest Normal University;Lanzhou New Area Municipal Investment Group Co., Ltd

关键词: Fully fourth-order boundary value problem;    Cantilever beam equation;    Nonlinear boundary condition;    Monotone iterative technique;    Lower and upper solutions;   

DOI  :  10.1186/s13662-021-03402-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The aim of this paper is to consider a fully cantilever beam equation with one end fixed and the other connected to a resilient supporting device, that is,$$ \textstyle\begin{cases} u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)), \quad t\in [0,1], \\ u(0)=u'(0)=0, \\ u''(1)=0,\qquad u'''(1)=g(u(1)), \end{cases} $$ where$f:[0,1]\times \mathbb{R}^{4}\rightarrow \mathbb{R}$ ,$g: \mathbb{R}\rightarrow \mathbb{R}$ are continuous functions. Under the assumption of monotonicity, two existence results for solutions are acquired with the monotone iterative technique and the auxiliary truncated function method.

【 授权许可】

CC BY