A Class Of Singularly Perturbed Problems Of Semilinear Elliptic Partial Differential Equations

Nonlinear partial differential equations have wide range of applications in various fields of natural science.Among them,the singularly perturbed problem of differential equations is of great importance to the research of physics,chemistry and biology.We study the singularly perturbed problem of elliptic equations with three different bound-ary conditions.The thickness of boundary layer and the asymptotic behaviour of so-lution on the boundary are analysed.The thesis can be divided into three parts.The first part is devoted to studying the problem with Dirichlet boundary condition,where we find the thickness of boundary layer and asymptotic behaviour for the boundary derivative of the solution by interior estimate and Pohozaev identity.The second part is focused on the problem with Robin boundary condition when the domain is radial and we will investigate the asymptotic behaviour of the solution on the boundary.In the third part,we study the problem with nonlinear Neumann boundary condition in the general domain.We will prove the boundedness of the solution and find an estimate for the solution by super and sub solution method.