On Asymptotic Behavior of Solutions of $$\boldsymbol{n}$$ th Order Emden–Fowler Type Difference Equations with Advanced Argument
2021
We study oscillatory properties of solutions of the Emden–Fowler type difference equation $$\Delta^{(n)}u(k)+p(k)\big{|}u\left(\sigma(k)\right)\big{|}^{\lambda}\textrm{sign}u\left(\sigma(k)\right)=0$$
, where $$n\geq 2$$
, $$0<\lambda<1$$
, $$p:\mathbb{N}\to\mathbb{R}_{+}$$
, $$\sigma:\mathbb{N}\to\mathbb{N}$$
and $$\sigma(k)\geq k+1$$
for $$k\in\mathbb{N}$$
. Sufficient conditions of new type for oscillation of solutions of the above equation are established. See analogous results for linear ordinary and nonlinear functional differential equations in [].
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