In this manuscript, two type of new oscillation criteria are obtained respect to coefficient ak in the following Eq. (1.1). In the subsection 2.1 considered as ak > 0. In the subsection 2.2 allowed it to be an oscillating sequence. There are no results for the oscillation of second order difference equations with oscillating coefficients up to now.
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In this paper we are concerned with the oscillation of solutions of higher-order sublinear neutral type difference equation with an o oscillating coefficient of the form [...] where p(k) is an oscillatory function which is interesting. We obtain some comparison criteria for oscillatory behaviour. The results are new when n =2 and n = 3.
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In this paper we are concerned with the oscillatory behaviour of solutions of a certain higher order nonlinear neutral type functional difference equation with oscillating coefficient. We obtain two sufficient criteria for oscillatory behaviour.
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Our aim in this paper is to obtain sufficient conditions under which certain difference equations have a "large" number of non-oscillatory solutions. Using the characteristic equation of a "majorant" delay difference equation with oscillating coefficients and Schauder's fixed point theorem, we obtain conditions under which the difference equation in question has a non-oscillatory solution.
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