Several Singularly Perturbed Problems With Nonlinear Boundary Value Conditions

In this thesis, several singularly perturbed problems with nonlinearboundary value conditions are mainly discussed. The article is structuredas follows:In chapter1, first of all, we sketch research significance and gener-al situation of singularly perturbed problems and summarize the studyachievements of singularly perturbed problems with nonlinear boundaryvalue conditions at home and abroad, which related to this thesis. Then,we state the critical methods and some important theories which we useand major works of this thesis.In chapter2, we consider a class of singularly perturbed problemwith two parameters and nonlinear two points boundary conditionsFirst of all, the formal asymptotic expansion of solution of the problem isconstructed by using the method of composite expansion on two variable.Then according to the theory of diferential inequalities, the existence ofsolution to the problem and the asymptotic behavior of the expansionare proved.In chapter3, we consider a class of singularly perturbed problem fornonlinear equation with nonlinear three points boundary value conditionsUsing the stretched variable and the method of composite expansion,aformal approximation of the solution of the problem is constructed. Thenaccording to the theory of diferential inequalities, the existence of solu-tion to the problem and the uniformly validity of the expansion in thediscussion area are proved.In chapter4, we give two examples which illustrate the applyingvalue of the study achievements that come from the second chapter andthe third chapter.