The Boundedness Of Solutions For A Class Of Higher Order Nonlinear Differential Integral Equations With Deviating Arguments

In this paper,we mainly discuss the boundedness of solutions of a class of higher order nonlinear integro-differential equations with deviating arguments.The thesis is divided into three sections according to the contents:In the first chapter,the historical background and research status of these problem are introduced.In the second chapter,with the aid of the new integral inequality,with suitable assump-tions,we mainly discuss the boundedness of solutions of a class of higher order nonlinear integro-diffeerential equations with deviating argumentsthe conclusions are as followsTheorem2.3.1suppose that fv(t),gj(t),ki(t) and P(t) are nonnegative continuous func-tions which defined on the [a,∞), v= 1,2,...l,j= 1,2,... = 1,2,...m.(?)(t) is continu-ously differentiable function,and satisfy (?)(t)≤ t,(?)’(t)> 0. limt→∞(t)> a. rv,qj,pi∈(0,1]is constant, and if you still haveset up,this is to say,for the any one of the initial function θ(t) which definded on the[r, a],the equation (2.1.1) have a solution x(t) on the [r,a] ∪ [a, ∞) and satisfy the initial conditions x(t) = θ(t), t∈[r, a] D0(x;p0)(t) is a bounded on the [a,∞)。Theorem2.3.2 suppose that F(t,x,y) as the theoreml,and in addition to condi-tion(3.1.3)(3.1.4)(3.1.5)still satifythen for each equation(2.1.1)anyone of the solutionsx(t), there are D0(x;p0)(t) when t→∞ have a finite limit。In particular, any solution x(t) of (2.1.1) , D0(x;p0)(t) tending to zero when t→∞.In the third chapter,with suitable assumptions,we mainly discuss the boundedness of solutions of a class of higher order nonlinear integro-differential equations with deviating argumentsthe consultion as followsTheorem3.3.1Suppose thatg(t)≤t and there are nonnegative continuous functionsqi(t), 0≤i≤n, and ψ(t) on[a, ∞), and wi(u) ∈ F, 0 ≤ i ≤ n -1, such that and Suppose moreover that and Then every solution x(t) of (3.1.2) satifies Lkx(t)=O(Jn-k-1(t)),t→∞,k=0,1,2,...n-1.Theorem3.3.2.Suppose that g(t)≤t and there are nonnegative continuous functions qi(t), 0≤i≤n, and ψ(t) on[a,∞), and wi(u) ∈ F,0≤i≤n-1, such that and Suppose moreover that 1<i<n-1.Then every solution x(t) of (3.1.2) satisfies Lkx(t)→0,0≤k≤n-1.