INTERVAL OSCILLATION CRITERIA FOR SECOND-ORDER DELAY AND ADVANCED DIFFERENCE EQUATIONS

INTERVAL OSCILLATION CRITERIA FOR SECOND-ORDER DELAY AND ADVANCED DIFFERENCE EQUATIONS

Interval oscillation criteria are established for second-orderdiğerence equations in the form(k (n)x(n)) +p (n) x (g (n)) +q (n) jx (g (n))jn; n02 N = f0; 1; :::g;1x (g (n)) =e (n) ;(E ) wherenquences of real numbers;k (n) > 0is nondecreasing;g(n)is nondecreasing,limn 1g(n) = 1:Several oscillation criteria are given for equation(E )considered as to separate delay and advanced diğerence equationswheng(n) < nandg(n) > nrespectively. Illustrative examples are included