Angular Layer Phenomena On Several Classes Of Singularly Perturbed Nonlinear Boundary Value Problems

The main content of this article is to study angular layer phenomena on several classes singularly perturbed problems. The basic structure of this thesis is as follows:In the first chapter, we mainly illustrate research general situation of singularly perturbed problem, and introduce the main work and the innovation of this thesis, then we state some necessary concepts and lemmas.In the second chapter, we mainly discuss angular layer solutions of singularly perturbed problems of a class of second order differential eduations We construct specific upper and lower solutions in three different condi-tions about the right function by introducing auxiliary problems, then prove the existence of the solutions and give the asymptotic estimate of solutions by the theory of differential inequality. Finally, three examples are given to illustrate application value of the results.In the third chapter, we consider angular layer behaviors of the singularly perturbed Dirichlet problems for a class of quasilinear second order differential equations with two parameters Constructing corresponding bounding functions in three different cases about the two small parameters. The existence of the solutions is proved and the asymptotic estimate of solutions is given by using the theory of differential inequalities. Finally, an example is given to illustrate signifi-cance of the results.In the fourth chapter, we mainly talk about boundary layer be-haviors and angular layer behaviors of the. singularly perturbed Robin problems for a class of quasilinear second order differential equations and Using the theory of differential inequalities, we prove the existence of the solutions, and give the asymptotic estimate of solutions for above problems in three different cases about the two small parameters.