Existence of monotone solutions to some singular boundary and initial value problems (Q1901105)

The author considers the differential equation \(y'' + f(t,y,y') = 0\) on \([0,1]\) with the boundary conditions \(y(0) = 0\), \(y(1) = a > 0\) or the initial condition \(y(0) = 0\), \(y' (0) = a > 0\). Here \(f\) is a nonnegative function which may be singular as \(y\downarrow 0\). Sufficient conditions to guarantee existence of nondecreasing solutions of this problem are established. A method uses an integral operator with a parameter.