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On a functional integrability and asymptotic properties of some nonlinear ordinary differential equations. (English) Zbl 0807.34060

Farkas, M. (ed.) et al., Differential equations and its applications. Proceedings of the colloquium on differential equations and applications, held in Budapest, August 21-24, 1991. Amsterdam: North-Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 62, 353-358 (1991).
This paper is concerned with a nonlinear differential equation of the form \(x''(t)+ a(t) x^ \alpha(t)= h(t)\), where \(a(t)\) and \(h(t)\) are continuous functions in \(t\in [t_ 0,\infty)\), and \(\alpha\) is a positive constant. The author only considers those solutions which belong to the space \(L_ p[t_ 0,\infty)\), and presents some asymptotic properties of the solutions under some additional conditions.
For the entire collection see [Zbl 0792.00006].

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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