Sharp Oscillation Criteria for Fourth Order Sub-half-linear and Super-half-linear Differential Equations

This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation (E) (p(t)vertical bar 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 satisfying conditions integral(infinity)(a) (t/p(t))(1/alpha) dt < infinity, integral(infinity)(a) t/(p(t))(1/alpha) dt < infinity. We will establish necessary and sufficient condition for oscillation of all solutions of the sub-half-linear equation (E) (for beta < alpha) as well as of the super-half-linear equation (E) (for beta > alpha).