Search

In this paper, we prove some new dynamic inequalities on time scales using Hölder's inequality and Keller's chain rule on time scales. These inequalities, as special cases when the time scale [ABSTRACT FROM AUTHOR]

In this paper, we will establish some new interval oscillation criteria for the forced second-order nonlinear dynamic equation[image omitted] on a time scale  where γ ≥ 1. As a special case when  =  our results not only include the oscillation results for second-order differential equations established by Wong (Oscillation criteria for a forced second-order linear differential equation, J. Math. Anal. Appl. 231 (1999), pp. 233-240) and Nasr (Sufficient condition for the oscillation of forced super-linear second order differential equations with oscillatory potential, Proc. Amer. math. Soc. 126 (1998), pp. 123-125) but also improve these results. When  = ,  = h or  = qN, i.e. for difference equations, generalized difference equations or q-difference equations our results are essentially new and also can be applied on different types of time scales, as illustrated in several examples. [ABSTRACT FROM AUTHOR]