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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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