On regular solutions of an equation of the Emden-Fowler type. (Russian) Zbl 0792.34032

Sadyrbaev, F. Zh.

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].

Reviewer: M.G.Filippov (Kiev)

MSC:

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

Keywords:

oscillating solution; characteristic values; Nehari’s solutions

Citations:

Zbl 0097.295