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Oscillation theorems for second-order nonlinear neutral differential equations. (English) Zbl 1236.34092

Summary: The purpose of this paper is to study the oscillation of the second-order neutral differential equations of the form

(a(t)[z ' (t)] γ ) ' +q(t)x β (σ(t))=0,

where z(t)=x(t)+p(t)x(τ(t)). We explore properties of given equations by examining those of associated first-order delay equations. New comparison theorems essentially simplify the examination of the equations studied as they allow us to deduce the oscillation of the second-order delay differential equation by applying the oscillation criteria obtained to the first-order delay equations. The results obtained are easy to verify.

MSC:
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
34K12Growth, boundedness, comparison of solutions of functional-differential equations
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