On A Singular Nonlinear Elliptic Problem

This thesis for Master's degree considers a singular nonlinear elliptic equationwhereΩis a bounded domain in Rn, n≥2, with C^2,β boundary (?),β∈(0,1), and K₁(x), K₂(x)∈C^2,β(?),α₁,α₂, p∈(0,1),λis a real parameter.The organization of this thesis is as the following:The chapter 1 is the introduction. We mainly consider the background, the recent development of the problem and some required prior knowledge.In chapter 2, we consider some of the nature of the above equation when K₁^*, K₂^*≤0(see definition on page 2) and K₁^* + K₂^*＜0, K₁1(x),K₂(x)＞0. We use the super-subsolution principle, maximal principle and approximation theory to know the existence, monotonicity with respect toλ, the boundary behaviour and the regularity of solutions.In chapter 3, we study the existence and the property of solutions By using a similar method when K₁(x), K₂(x) satisfy the other conditions.