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Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference operator

In: Mathematica Slovaca, vol. 66, no. 3
Yaşar Bolat - Ömer Akin

Details:

Year, pages: 2016, 677 - 686
Keywords:
oscillation, difference equaions, generalized difference, half-linear difference equation
About article:
In this paper, oscillation criteria are obtained for higher-order half-linear delay difference equations involving generalized difference operator of the form $$ \Delta_b(p_n(\Delta_b^{m-1}x_n)^{\alpha}) +q_n x_{n-\sigma}^{\beta}=0, n\geq n_0, $$ where $\Delta_{b}$ is defined by $\Delta_b y_n = y_{n+1}-by_n$, $b\in\mathbb{R}-\{0\}$, $p:\mathbb{N}\to \mathbb{R}^+$, $\alpha$, $\beta$ are the ratio of odd positive integers with $\beta \leq \alpha$; $m$, $n$, $n_0$, $\sigma$ are non-negative integers, $q:\mathbb{N}\rightarrow\mathbb{R}$. The cases of $b$ negative and positive and $q_n \geq 0$, which has important role for oscillation of this equation, are considered. Also we provide some examples to illustrate our main results.
How to cite:
ISO 690:
Bolat, Y., Akin, Ö. 2016. Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference operator. In Mathematica Slovaca, vol. 66, no.3, pp. 677-686. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0169

APA:
Bolat, Y., Akin, Ö. (2016). Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference operator. Mathematica Slovaca, 66(3), 677-686. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0169
About edition:
Published: 1. 6. 2016