On the oscillatory behaviour of solutions of second order nonlinear difference equations
The authors consider the difference equation (1) \(\Delta (a_ n \Delta y_ n) + q_{n + 1} f(y_{n + 1}) = r_ n\), \(n \in N_ 0\). All values in (1) are real. A solution \(\{y_ n\}\) of (1) is said to be oscillatory if it is neither essentially positive nor essentially negative. Sufficient conditions for the solution \(\{y_ n\}\) of (1) to be oscillatory or \(\liminf_{n \to \infty} | y_ n | = 0\) are established. Sufficient conditions for oscillation of all solutions of equation (1) when \(r_ n = 0\) for all \(n \in N_ 0\) are obtained.
second order nonlinear difference equations
scientific article; zbMATH DE number 605112