On Asymptotic Behavior of Solutions of $$\boldsymbol{n}$$ th Order Emden–Fowler Type Difference Equations with Advanced Argument

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 [].