Abstract
In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of higher-order difference equations involving the generalized difference operator of the form $\Delta _{a}^{k}(p_{n}\Delta _{a}^{2}y_{n})=f(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n}),$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
Highlights
In this paper, we study nonoscillation and oscillation of solutions of a class of higher-order difference equations of the form∆ka(pn∆2ayn) = f (n, yn, ∆ayn, ..., ∆ka+1yn), n ∈ N, (1)where N is the set of natural numbers, a ∈ R\{0}, R is the set of real numbers, {pn} is a real sequence with pn= 0 for n ∈ N and f : N × Rk+2 −→ R
Sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of higher-order difference equations involving the generalized difference operator of the form
We study nonoscillation and oscillation of solutions of a class of higher-order difference equations of the form
Summary
We study nonoscillation and oscillation of solutions of a class of higher-order difference equations of the form. In [4], Agarval et al established sufficient conditions for the oscillation of all solutions of the even order difference equations of the form. In [12], Popenda obtained sufficient conditions for nonoscillation/oscillation of solutions of a class of nonlinear nonhomogeneous second order difference equations involving generalized difference of the form. In [10], Parhi and Panda obtained sufficient conditions for nonoscillation /oscillation of all solutions of a class of nonlinear third order difference equations of the form. Our purpose is to establish oscillation and nonoscillation criteria for a class of higher-order difference equations involving generalized difference operator of the form Eq (1)
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