Positive solutions of nonlinear singular boundary value problem in abstract space (Q1767784)

The authors investigate the boundary value problem \[ x''(t)+f(t,x(t))=\theta, t\in (0,1),\quad x(0)=x(1)=\theta, \tag{P} \] in a Banach space \(E\), where \(f\) has singularities at \(t=0\), \(t=1\) and \(x=\theta\). Under suitable assumptions on \(f\), using the Mönch fixed-point theorem, the existence of a positive solution to (P) is proved. An example -- an infinite-dimensional singular differential system, is also presented.