SHARP OSCILLATION CRITERIA FOR A CLASS OF FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS

This paper is concerned with the oscillatory and the nonoscillatory behavior of the fourth-order nonlinear differential equation (Delta) (p(t)x ''vertical bar(alpha-1)x '')'' + q(t)vertical bar x vertical bar(beta-1)x = 0, where alpha > 0, beta > 0 are constants and p,q : [a, infinity) -> (0, infinity) are continuous functions. We will establish necessary and sufficient condition for oscillation of all solutions of sub-half-linear equation (Delta) (for beta < alpha) as well as of super-half-linear equation (Delta) (for beta > alpha).