Nonoscillatory solutions for super-linear Emden-Fowler type dynamic equations on time scales

In this paper, we consider the following Emden-Fowler type dynamic equations on time scales (a(t) vertical bar x(Delta)(t)vertical bar(alpha) sgn x(Delta) (t) )(Delta) + b (t) vertical bar x (t) vertical bar (beta) sgn x (t) = 0, when alpha < beta. The classification of the nonoscillatory solutions are investigated and some necessary and sufficient conditions of the existence of oscillatory and nonoscillatory solutions are given by using the Schauder-Tychonoff fixed point theorem. Three possibilities of two classes of double integrals which are not only related to the coefficients of the equation but also linked with the classification of the nonoscillatory solutions and oscillation of solutions are put forward. Moreover, an important property of the intermediate solutions on time scales is indicated. At last, an example is given to illustrate our main results.