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On regular solutions of an equation of the Emden-Fowler type. (Russian) Zbl 0792.34032
Klokov, Yu. A. (ed.), Theoretical and numerical studies on boundary value problems. Collection of scientific works. Riga: Latvijskij Gosudarstvennyj Universitet Im. P. Stuchki, 19-25 (1989).
The author gives the conditions of existence of a nontrivial regular \((\equiv \) continuable on \([t_ 0,+\infty))\) solution of the equation \(y''+p(x)| y |^{2 \varepsilon} y=0\), \(\varepsilon>0\) with continuous and positive function \(p(x)\). This conditions are formulated in terms of the Nehari’s solutions (see Z. Nehari [Trans. Am. Math. Soc. 95, 101-123 (1960; Zbl 0097.295)]).
For the entire collection see [Zbl 00054359].
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations