OSCILLATION AND NONOSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS OF EULER TYPE

摘要

This paper deals with the oscillatory behavior of solutions of difference equations corresponding to second-order nonlinear differential equations of Euler type. The obtained results are represented as a pair of oscillation and nonoscillation criteria, and are best possible in a certain sense. Linear difference equations corresponding to the Riemann-Weber version of the Euler differential equation and its extended equations play an important role in proving our results. The proofs of our results are based on the Riccati technique and the phase plane analysis of a system.