Kamenev-type oscillation criteria for second order nonlinear dynamic equations on time scales

摘要

The purpose of this paper to establish oscillation criteria for second order nonlinear dynamic equation(r(t)(xΔ(t))γ)Δ+f(t,x(g(t)))=0,on an arbitrary time scale T, where γ is a quotient of odd positive integers and r is a positive rd-continuous function on T. The function g:T→T satisfies g(t) ⩾ t and limt→∞g(t) = ∞ and f∈C(T×R,R). We establish some new sufficient conditions such that the above equation is oscillatory by using generalized Riccati transformation. Our results in the special cases when T=R and T=N involve and improve some oscillation results for second-order differential and difference equations; and when T=hN,T=qN0 and T=N2 our oscillation results are essentially new. Some examples illustrating the importance of our results are included.