Positive solutions of singular problems with sign changing Carathéodory nonlinearities depending on \(x'\) (Q1874619)

The existence of positive Carathéodory solutions is proved to some second-order problem. The right-hand side is a Carathéodory function which may be singular at a certain phase point. Moreover, it can change sign. One of the boundary conditions is nonlinear and rather implicit. The combination of upper/lower solutions technique is applied jointly with degree arguments.