Multiple positive solutions to singular boundary value problems for superlinear higher-order ODEs (Q1586284)

The author discusses the \((k,n-k)\) conjugate boundary value problem \[ (-1)^{n-k} y^{(n)}=f(t,y),\quad 0<t<1, \] \[ y^{(i)}(0)=0, \quad 0\leq i\leq k-1,\quad y^{(j)}(1)=0,\quad 0\leq j\leq n-k-1. \] Here, the nonlinearity \(f\) may be singular at \(t=0\), \(t=1\) and \(y=0\). Existence of multiple solutions is established via Krasnoselskij's fixed-point theorem in a cone.