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On some classes of continuable solutions of a nonlinear differential equation. (English) Zbl 0827.34020

Authors’ summary: “The aim of this paper is to present a global qualitative analysis for the asymptotic behaviour of the solutions of the nonlinear equation \([r(t) x']'+ q(t) f(x)= 0\), \(\left('= {d\over dt}\right)\), where \(r\), \(q: [0, +\infty)\to \mathbb{R}\), \(f: \mathbb{R}\to \mathbb{R}\) are continuous functions, \(r(t)> 0\), \(q(t)> 0\) and \(u\cdot f(u)> 0\) for \(u\neq 0\)”.

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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