On Lyapunov-type inequalities for nonlinear dynamic systems on time scales

In this paper, by using elementary analysis, we establish several new Lyapunov type inequalities for the following nonlinear dynamic system on an arbitrary time scale TT{xΔ(t)=α(t)x(σ(t))+β(t)|y(t)|p−2y(t),yΔ(t)=−γ(t)|x(σ(t))|q−2x(σ(t))−α(t)y(t), when the end-points are not necessarily usual zeros, but rather, generalized zeros, which generalize and improve all related existing ones including the continuous and discrete cases.