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Oscillation of Second Order Functional Difference Equations of Non-canonical Type

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Abstract

The main goal of the work is to study the necessary and sufficient conditions for the oscillation of solutions of second order neutral difference equations of the form:

$$\begin{aligned} \Delta [a(n)\Delta (x(n)+r(n)x(\tau (n))] +p(n)G(x(\sigma (n)))=0. \end{aligned}$$

Here, we assume that the non-linear function is either strongly sublinear or strongly superliner. Some examples are given to illustrate our main results.

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  1. Department of Mathematics, Sambalpur University, Sambalpur, 768019, India

    G. N. Chhatria

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  1. G. N. Chhatria
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Correspondence to G. N. Chhatria.

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This work is supported by Rajiv Gandhi National fellowship(UGC), New Delhi, India, through the Letter No. F1-17.1/2017-18/RGNF-2017-18-SC-ORI-35849, dated. 11th July, 2017.

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Chhatria, G.N. Oscillation of Second Order Functional Difference Equations of Non-canonical Type. Mediterr. J. Math. 18, 253 (2021). https://doi.org/10.1007/s00009-021-01882-7

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  • DOI: https://doi.org/10.1007/s00009-021-01882-7

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