Several Classes Singularly Perturbed Boundary Value Problems For Nonlinear Third Order Differential Equations

In this thesis,the existence and asymptotic behavior of solutions for several classes singularly perturbed boundary value problems of nonlinear third order dif-ferential equations are mainly considerd.The thesis is divied into four chapters.In the first chapter,we sketch research general situation and research signifiance of singularly perturbed problems,then we summarize the study achievements of sin-gularly perturbed problems for three order differential equations and second order differential equations with quadratic dependence on the first derivative at home and abroad.Lastly, we state the critial methods, some important theories that we use and the main works in this thesis.In the second chapter,the formal asymptotic expansions of solutions for a class of singularly perturbated boundary value problems of three order differential equa-tions with quadratic dependence on the second derivative are obtained by using the method of composite expansion.The existence of solutions for the original problems and the uniformly validity of the obtained formal asymptotic solutions are proved under suitable assumptions according to the fixed point theorem.In the third chapter,the approximation of solutions for a class of singularly perturbated problems of the weaker nonlinear third order differential equations are obtained by using the method of composite expansion. The uniformly validity and asymptotic behavior for the approximation of solutions are disscussed according to the theory of differential inequality.In the last chapter, the formal asymptotic expansions of solutions for a class of singularly perturbation for three points mixed boundary value problems of nonlinear third order differential equations are obtained by using the method of composite expansion.The existence of solutions for the original problems and the uniformly validity of the obtained formal asymptotic solutions are proved according to the theory of differential inequality.