Oscillation Criteria for a Family of Second Order Nonlinear Difference Equations with Continuous Arguments

Abstract

Oscillation criteria for a family of second order nonlinear difference equations with continuous arguments is studied by theory of oscillation.Then some sufficient conditions for the oscillations of all solutions and first order difference of solutions of this equation are established.Using the fixed point theorem in Banach space,the non-oscillatory solution of the equation is studied and positive solution of the equation in special conditions is obtained.