Research On Several Problems Of Differential Equations

1,The oscillatory properties of a kind of second2order nonlinear differential equation where 0≤β<1 is a constant are considered. Using the average behavior of the integral and Hardy , Littlewood & Polya inequality , it builds some oscillation criteria for equation (1.1) and extends some known oscillation criteria to more general equations. Meanwhile , the proof process of Manojlovic J V's article is improved.2,By means of constructing Liapunov functional V (t ,x(?)) ,we weak the conditions on V (t ,x(?)) and D + V(t ,x(?)). We obtain some sufficient conditions of stability of nonlinear Volterra integro-differential equation and improve some results in [9].3,In this paper,the sign of derivative of Liapunov function may be variable with some integral conditions. Some sufficient conditions of stability of nonautonmous system are obtained and some results in [13-16] are improved.