Oscillation for a second-order nonlinear integro-differential inequality is studied.Firstly,taking advantage of Lebesgue's deminated convergence theorem,the condition of the positive solution's existence for inequality is obtained;then the condition of the positive solution's inexistence for inequality is gained;finally,by using of discussion and analysis,the sufficient and necessary condition of it is derived.

In this paper,we investigate the influence of small prime pf-value on the structures of the finite groups,and give a complete classification.Some new results are gained.Let G be a finite group.If pf(G)=1,then G is isomorphic to C2 or C3.LetG be a finite group.If pf(G)=2,then is G isomorphic to C4,C5 or C2×C2.Let G be an abelian group.If pf(G)=3,then G is isomorphic to C6,C9,C3×C3 or C2×C2×C2.

The general logistic biological model with discret delays and disturbs is investigated.First of all,according to the eigenvalue theory,the condition for the existence of bifurcation period solution is obtained;after that,the form of approximate period solution is derived by the conditions of the period function orthogonal;in the end,through examples,fitted curve figures are achieved by using Matlab when asign the different values to the parameters,and then the parameters of the model are discussed.

A linearized oscillation theory for a second-order differential equation with variable coefficients and constant delay was investigated.Firstly,by using the Knaster-Tarski fixed-point theorem,the linearized oscillation criterion of the equation was obtained as the variable coefficients in some range,then the condition as the variable coefficients in the different range was discussed,finally,the whole sufficient and necessary condition of it was derived,and so the oscillatin of the equation′s solution was simplified.