The Application Of The Fixed Point Theorem To Singularly Perturbed Problems

In this dissertation, the existence and asymptotic behavior of solutions for boundary value problems of singularly perturbed ordinary differential equations and 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 fixed point theorem. What is worth pointing out is that by applying the fixed point theorem, a class of boundary value problems for singularly perturbed ordinary differential equations which are very difficulty to deal with by using the method of differential equalities are studied.