Positive solutions of even higher-order singular superlinear boundary value problems.
The authors consider the following even higher-order nonlinear boundary value problem \[ \begin{aligned} (-1)^mu^{(2m)}(t)&= f(t,u(t),u''(t),\dots,u^{(2(m-1))}(t)), \quad 0<t<1,\\ u^{(2i)}(0)&= u^{(2i)}(1)=0, \quad i=0,\dots,m-1,\end{aligned}\tag{1} \] where \(m>1\) is an integer, \(f\in C((0,1)\times \mathbb{R}^+\times \mathbb{R}^-\times\cdots\times \mathbb{R}^{s_{m-1}},\mathbb{R}^+)\), where \(s_{m-1}\) is the sign of \((-1)^{m-1}\).
scientific article; zbMATH DE number 2017210