Oscillation And Stability For Several Class Of Nonlinear Differential Equations

In the first part of this paper, by using the Hardy-Littlewood-Polya inequality and a generalized Riccati technique, we established respectively some interval oscillation criteria of solutions for the second order half-linear ordinary differential equationand the second order nonlinear differential equationThese criteria differ from the existing oscillation results depending upon the information on the whole half-line of the equations and they are also applicable to the case that the function q(t) has a "bad" behavior on the most part of the interval [t₀,∞)(e.g., ∫_t0^∞ q(s)ds = -∞). Meanwhile, these results improve and extend most existing ones. In addition, some examples are also given in order to verify our theoretical results obtained here.In the second part of this paper, we investigate mainly the stability of the zero solution of the following first order linear functional differential equations with two discrete delays of the formBy constructing the suitable Lyapunov functionals, we established some Wazewski-type inequalities for the solutions of the above equation. We also obtain some sufficient conditions ensuring the zero solution of the above equation is asymptotically stable and unstable by applying these inequalities.