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Properties of solutions of higher order nonlinear difference equations. II. (English) Zbl 0599.39002
This is a continuation to part I [ibid. 31, 165-172 (1985; reviewed above)] on asymptotic and oscillatory properties of solutions of the nonlinear difference equation $(1)\quad \Delta^ n x(t)+f(t,\hat x(t))=0,\quad t\in I,$ where I is the discrete set $$\{0,1,...\}$$ and $$\hat x(t)$$ stands for $$(x(t),\Delta x(t),...,\Delta^{n-1} x(t))$$, $$\Delta$$ is the difference operator $$\Delta x(t)=x(t+1)-x(t)$$. Besides (1), we also consider its variant $\Delta^ n x(t)+p(t)g(t,\hat x(t))=h(t,\hat x(t)),\quad t\in I.$

##### MSC:
 39A10 Additive difference equations 39A12 Discrete version of topics in analysis
##### Keywords:
asymptotics; oscillations