Research On Dynamic Solutions Of Boundary Value Problems Taken A Few Classes

Ordinary diferential equations with layer boundary arise widely in many felds, likescience and technology and economic and so on. Various of methods in the asymptoticanalysis of singular perturbation can be used to solve problems validly, such so boundary layerfunction method, diferential inequality method, matched asymptotic expansion method,plane analysis method and so on. In this paper, by the theory of asymptotic expansion andmatched asymptotic expansion, we study the existence results of some classes of perturbedboundary value problem. Furthermore, we apply some of the existence results to singularperturbed boundary value problem which involve the missile dynamics model. The paperand the main content of the paper are as follows:In the chapter1, the historical development and some method in common use of singularperturbation are introduced.In the chapter2, a class of nonlinear speed system perturbed solution nonlocal problemis discussed in this paper．In appropriate conditions, frst constructed out external solution,again according to diferent boundary layer and using stretchy variable and power serieslaunched theory, the asymptotic expansions of solution of this problem is shown and provedto be uniformly efective using the theory of diferential inequality in the whole interval. Thispaper extends the perturbed problem of the parameters of the parameters of the promotionto multiple parameters．In the chapter3, the boundary value problem of nonlinear singular perturbed impulsivediferential equations with boundary layer atone end(left or right) point was discussed. Forthe method, the defned interval is divided into a series of subintervals and the solutions oneach subinterval are obtained．Namely, on the subinterval of boundary layer, we yield anexpansion by using matching techniques. Then, by using impulsive and boundary conditions,we obtain the solutions on other subintervals. Then, three examples were discussed to showthe application of the results．In the chapter4, based on the singular perturbation theory, try a combination of per- turbation theory and a missile longitudinal model. First, by perturbation method get theequilibrium point of the attitude motion of a missile longitudinal. At the same time, it isstable by Hurwitz criterion. A series of stability systems are found in dynamical equation byselecting diferent parameter matrixes of perturbed torque. And then the missile longitudinalof stability are found by using an approximate method.