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Oscillation of solutions to a neutral differential equation involving an \(n\)-order operator with variable coefficients and a forcing term. (English) Zbl 1298.34122

Summary: We study the oscillation of solutions to the neutral differential equation \[ \begin{aligned} \frac{d}{dt}( & |L_{n-1}(y(t)+p(t)y(\tau(t)))|^{\beta-1}L_{n-1}(y(t)+p(t)y(\tau(t))))\\ & +v(t)G(y(\delta(t)))-u(t)H(y(\sigma(t)))=f(t),\end{aligned} \] where \(L_i\) are differential linear operators with variable coefficients. We find sufficient conditions for all solutions to oscillate or to tend to zero as \(t\) approaches infinity. A difference equation which is analog of the above equation is also studied.

MSC:

34K11 Oscillation theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K40 Neutral functional-differential equations
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