Singular Perturbation Of Several Classes Of Nonlinear Differential Systems With Boundary Value Problem

The differential inequality theory and diagonalization method ,as two effective tools in solving singular perturbation problems ,have developed rapidly in the recent several decades . In this paper ,these two methods are employed to consider three kinds of singular perturbation boundary value problems .In the first section,the existence of solution for a class of non-linear systems with three -point boundary problem is obtained by applying the differential inequality theory .In the second section ,we use the differential inequality theory to discuss the non-monotone interior layer solution for one kind of singularly perturbed quasilinear boundary value problems with a turning point . In the third section,the diagonalization method is applied to study the existence of solution for a class of vector differential systems with two-point or three-point boundary problems .Meanwhile,the asymptotic estimate of the solution as well as its first-order derivative and its second-order derivative is obtained .