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Zbl 1207.34041
Došlý, Ondřej; Fišnarová, Simona
Half-linear oscillation criteria: perturbation in term involving derivative. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 12, 3756-3766 (2010). ISSN 0362-546X

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

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

Cited in: Zbl pre05910785

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