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Existence of solutions to some singular initial value problems. (English) Zbl 0646.34003
Existence of positive solutions of the initial value problem $$\psi (t)y''=f(t,y,y')$$, $$y(0)=\alpha \geq 0$$. $$y'(0)=\beta$$ is established, where $$\psi$$ may vanish at $$t=0$$ and f may be singular at $$y=0$$. Estimates for the size of the domain of maximally extended solutions are also given. Finally, we study existence of a solution of the similar first-order problem $$\psi (t)y'=f(t,y)$$, $$y(0)=\alpha$$ and estimate from below the domain of its definition.
Reviewer: L.E.Bobisud

##### MSC:
 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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##### References:
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