Oscillation and nonoscillation criteria for second order difference equations with generalized difference operators

In this study we investigate some new oscillation and nonoscillationcriteria and generalize and improve some results in the literaturesfor second order nonlinear difference equation with generalized difference operators of the form¢l;a(pn¢l;axn) + qn(¢l;axn)¯ = F (n; xn; ¢l;bxn);where ¢l;¾ is generalized difference operator such that defined as ¢l;¾xn =xn+l ¡ ¾xn, and F : N £ R2 ! _included. R. Also, some examples illustrating the results areAMS (MOS) Subject Classification Codes: 39A10; 39A21Key Words: Oscillation; nonoscillation; difference equation; generalized difference equation;generalized difference operator