Asymptotic formula for oscillatory solutions of some singular nonlinear differential equation. (English) Zbl 1222.34034

Rachůnková, Irena; Rachůnek, Lukáš

Abstr. Appl. Anal. 2011, Article ID 981401, 9 p. (2011).

Summary: The singular differential equation
\[ (p(t)u')' = p(t)f(u) \]
is investigated. Here, \(f\) is Lipschitz continuous on \(\mathbb R\) 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.

MSC:

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

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