Oscillation criteria for nonlinear difference equations with superlinear neutral term

Oscillation criteria for nonlinear difference equations with superlinear neutral term

In this paper, the authors obtain sufficient conditions for the oscillation of all solutions of the equation$$\Delta\left(a_n \Delta\left(x_n+p_n x_{n-k}^\alpha\right)\right)+q_n x_{n+1-l}^\beta=0$$where $\alpha \geq 1$ and $\beta>0$ are ratio of odd positive integers, and $\left\{a_n\right\},\le...

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Veröffentlicht in:Malaya journal of matematik 2017-07, Vol.5 (3), p.580-586
Hauptverfasser: B. Kamaraj, R. Vasuki
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description In this paper, the authors obtain sufficient conditions for the oscillation of all solutions of the equation$$\Delta\left(a_n \Delta\left(x_n+p_n x_{n-k}^\alpha\right)\right)+q_n x_{n+1-l}^\beta=0$$where $\alpha \geq 1$ and $\beta>0$ are ratio of odd positive integers, and $\left\{a_n\right\},\left\{p_n\right\}$ and $\left\{q_n\right\}$ are real positive sequences. Examples are provided to illustrate the importance of the main results.
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title Oscillation criteria for nonlinear difference equations with superlinear neutral term
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