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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 \[ (a(t)[z'(t)]^{\gamma })'+q(t)x^{\beta }(\sigma (t))=0, \] where \(z(t)=x(t)+p(t)x(\tau(t))\). 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:
34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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