Oscillation of second-order nonlinear forced dynamic equations with damping on time scales

Abstract

In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second-order nonlinear forced dynamic equation with damping on a time scale T$$(r(t)g(x^{\Delta}(t)))^{\Delta} + p(t)g(x(t)) + q(t)f(x^{\sigma}(t)) = G(t; x^{\sigma}(t));$$where $r(t), p(t)$ and $q(t)$ are real-valued right continuous functions on T and no sign conditions are imposed on these functions. The function $f : T \to T$ is continuouslydifferentiable and nondecreasing such that $xf(x) > 0$ for $x \neq 0$. Our results not only generalize and extend some existing results, but also can be applied to the oscillationproblems that are not covered in literature. Finally, we give some examples to illustrateour main results.