×

zbMATH — the first resource for mathematics

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