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Properties of solutions of higher order nonlinear difference equations. I. (English) Zbl 0599.39001
We discuss asymptotic and oscillatory properties of solutions of nonlinear difference equation \[ \Delta^ n x(t)+f(t,x(t),\Delta x(t),...,\Delta^{n-1} x(t))=0,\quad t\in I \] and its variant \[ \Delta^ n x(t)+p(t)F(x(t),\Delta x(t),...,\Delta^{n-1} x(t))=0,\quad t\in I, \] where I is the discrete set \(\{\) 0,1,...\(\}\) and \(\Delta\) is the difference operator \(\Delta x(t)=x(t+1)-x(t)\).

MSC:
39A10 Additive difference equations
39A12 Discrete version of topics in analysis
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