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Existence of monotone solutions to some singular boundary and initial value problems. (English) Zbl 0836.34020
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.
##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations