Oscillation properties of an Emden-Fowler type equation on discrete time scales

In this paper, we explore the oscillation properties of u(Delta2)(t)+p(t)u(gamma)(sigma(t)) = 0 on a time scale T with only isolated points, where p( t) is defined on T and g is a quotient of odd positive integers. We define oscillation in this setting, and generate conditions on the integral of p(t) which guarantee oscillation and find conditions which give the existence of a nonoscillatory solution. In addition, we consider the case when solutions of this equation has asymptotically positively bounded differences.