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Asymptotic behavior of positive solutions of sublinear differential equations of Emden-Fowler type. (English) Zbl 1228.34072

Summary: We are concerned with an asymptotic analysis of positive solutions of the second-order nonlinear differential equation (A) \(x''(t)+q(t)\varphi (x(t))=0\), where \(q:[a,\infty )\to (0,\infty )\) is a continuous function which is regularly varying and \(\varphi:(0,\infty )\to (0,\infty)\) is a continuous increasing function which is regularly varying of index \(\gamma \in (0,1)\). An application of the theory of regular variation gives the possibility of determining precise information about the asymptotic behavior at infinity of intermediate solutions of Eq. (A).

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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