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Asymptotic formula for oscillatory solutions of some singular nonlinear differential equation. (English) Zbl 1222.34034
Summary: The singular differential equation $$(p(t)u')' = p(t)f(u)$$ is investigated. Here, $f$ is Lipschitz continuous on $\Bbb R$ and has at least two zeros 0 and $L > 0$. The function $p$ is continuous on $[0,\infty)$ and has a positive continuous derivative on $(0,\infty)$ and $p(0) = 0$. An asymptotic formula for oscillatory solutions is derived.

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34D05Asymptotic stability of ODE
Full Text: DOI
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