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Zbl 1217.34054
Došlý, Ondřej; Fišnarová, Simona
Two-parametric conditionally oscillatory half-linear differential equations. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 182827, 16 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We study perturbations of the nonoscillatory half-linear differential equation $$(r(t)\Phi(x'))'+c(t)\Phi(x)=0,$$ $\Phi(x):=|x|^{p-2}x,$ $p>1$. We find explicit formulas for the functions $\widehat r$, $\widehat c$ such that the equation $$[(r(t)+\lambda\widehat r(t)) \Phi(x')]'+[c(t)+\mu\widehat c(t)] \Phi (x)=0$$ is conditionally oscillatory, that is, there exists a constant $\gamma$ such that the previous equation is oscillatory if $\mu-\lambda>\gamma$ and nonoscillatory if $\mu-\lambda <\gamma$. The obtained results extend previous results concerning two-parametric perturbations of the half-linear Euler differential equation.

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: nonoscillatory half-linear differential equation; two-parametric perturbations; Euler differential equation

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Zentralblatt MATH Berlin [Germany]