Half-linear oscillation criteria: perturbation in term involving derivative. (English) Zbl 1207.34041

Došlý, Ondřej; Fišnarová, Simona

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 12, 3756-3766 (2010).

Summary: We consider the non-oscillatory half-linear differential equation
\[ (r(t)\Phi(x'))'+c(t)\Phi(x)=0,\quad \Phi(x):=|x|^{p-2}x,\quad p>1, \]
and we study the oscillatory properties of its perturbation
\[ [(r(t)+\widetilde r(t))\Phi(x')]'+(c(t)+\widetilde c(t))\Phi(x)=0.\tag{*} \]
We use the Riccati technique and the relationship between (*) and a certain associated linear equation. The results are applied to a perturbed Euler-type equation.

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

half-linear differential equation; oscillation and nonoscillation criteria; Riccati technique; perturbation principle; linearization method

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