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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.
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