A Class Of Singularly Perturbed Problems Dealt With Two Important Methods

In this dissertation, the existence and asymptotic behavior of solutions for boundary value problems of singularly perturbed ordinary differential equations and nonlocal elliptic equations as well as singularly perturbed reaction diffusion problems are mainly considered. On the basis of the formal asymptotic solutions having been constructed for the singularly perturbed problems, the formal asymptotic solutions for the original problems are proved by using the differential inequalities and the fixed point theorems. What is worth pointing out is that in 2.1 a class of singularly perturbed second order ordinary differential equations with nonlinear boundary value condi- tions are discussed by using the method of differential inequalities; In 2.2 introduce two small parameters into partial differential equations and obtain the result accordingly; What's more, consider nonlocal problem for ordinary and partial differential equations.