Positive solutions of \(2m\)th-order boundary value problems
By application of the Guo-Krasnosel'skii fixed-point theorem in a cone, the authors prove the existence of a positive solution to two boundary values problems for the equation \[ (-1)^m y^{(2m)}(t)=f(t, y(t), y''(t), \ldots, y^{2(m-1)}(t)), \] where \(f\) is either superlinear or sublinear. The boundary conditions are \[ \begin{aligned} y^{2 i}(0)&= 0=y^{2 i}(1), \quad 0 \leq i \leq m-1, \qquad\text{ or }\\ y^{2 i}(0)&= 0=y^{2 i +1 }(1), \quad 0 \leq i \leq m-1.\end{aligned} \] {}.
scientific article; zbMATH DE number 1794944