Oscillation and asymptotic behavior of second order difference equations. (English) Zbl 0780.39006

Zhang, B. G.

J. Math. Anal. Appl. 173, No. 1, 58-68 (1993).

For certain difference equations of the form \(\Delta(c_ n\Delta y_ n)+p_ ny^ k_{n+1}=0\) \((n\geq 0\), \(k\) a quotient of odd positive integers) conditions are obtained which are equivalent to the fact that all solutions are oscillatory. Moreover, certain conditions are derived under which all nonoscillatory solutions of the difference equation \(\Delta^ 2y_{n-1}+p_ ny_ n=f_ n\) \((n\geq 1)\) eventually tend to zero.

Reviewer: H.Länger (Wien)

MSC:

39A10

Additive difference equations

Keywords:

second order difference equation; oscillation; convergence to zero