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Comparison and oscillatory behavior for certain second order nonlinear dynamic equations. (English) Zbl 1219.34115

The authors consider the second order nonlinear dynamic equation

a(x Δ ) α Δ (t)+q(t)x β (t)=0

on an arbitrary time scale 𝕋, where α and β are ratios of positive odd integers, a and q are positive rd-continuous functions on 𝕋. They establish comparison results with the inequality

a(x Δ ) α Δ (t)+q(t)x β (t)0

which are applied to neutral equations. A necessary and sufficient condition is obtained for the oscillation property of second order equations on time scales.

MSC:
34N05Dynamic equations on time scales or measure chains
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
References:
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