Oscillation of Second-Order Nonlinear Forced Functional Dynamic Equations with Damping Term on Time Scales

Abstract

. In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term r )) σ t )) ) p t ) t ))) t ) , and ( r ( t ) x ∆ ( t )) ∆ + q ( t ) x ( t ) + p ( t ) f ( x ( σ ( t ))) = e ( t ) , on a time scale T , where r ( t ), p ( t ) and q ( t ) are real-valued right-dense continuous (rd-continuous) functions [1] defined on T with p ( t ) < 0 and τ : T → T is a strictly increasing differentiable function and lim t →∞ τ ( t ) = ∞ . No restriction is imposed on the forcing term e ( t ) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.