Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations
The authors establish sufficient conditions for the oscillation of all solutions of the perturbed difference equation \[ \Delta(a_{n- 1}(\Delta y_{n- 1})^ \sigma)+ F(n, y_ n)= G(n, y_ n, \Delta y_ n),\quad n\geq 1 \] as well as for the existence of a positive monotone solution of the damped difference equation \[ \Delta(a_ n(\Delta y_ n)^ \sigma)+ b_ n(\Delta y_ n)^ \sigma+ H(n, y_ n, \Delta y_ n)= 0,\quad n\geq 0, \] where \(0< \sigma= p/q\) with \(p\), \(q\) odd integers, or \(p\) even and \(q\) odd integer. For related results see the reviewer [Comput. Math. Appl. 28, No. 1-3, 309-316 (1994; Zbl 0807.39002)] and \textit{H. J. Li} and \textit{S. S. Cheng} [Tamkang J. Math. 24, No. 3, 269-282 (1993; Zbl 0787.39005)].
second-order nonlinear difference equations
scientific article; zbMATH DE number 749343
scientific article