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

Abstract The aim of this paper is to consider a fully cantilever beam equation with one end fixed and the other connected 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} { u ( 4 ) t = f , ′ ″ ‴ ∈ [ 0 1 ] g where $f:[0,1]\times \mathbb{R}^{4}\rightarrow \mathbb{R}$ : × R → , $g: \mathbb{R}\rightarrow are continuous functions. Under assumption monotonicity, two existence results for solutions acquired monotone iterative technique auxiliary truncated function method.