Singular mixed boundary value problem (Q2493004)

A singular nonlinear boundary value problem is studied in the form \[ u''+f(t,u, u')=0, \quad u'(0)=0,\quad u(T)=0. \] The nonnegative nonlinearity \(f\) is defined on \((0,T)\times(0,\infty)\times x(-\infty,0)\) and can have singularities. Sufficient conditions are given for the existence of a positive solution. The considerations are based on the technique of lower and upper functions. An illustrative example is given.