حسن, د. ابراهيم محمد2025-03-132025-03-13https://dspace.academy.edu.ly/handle/123456789/1484In this dissertation we have to consider solution of linear and quasi-linear second order partial differential equations of elliptic type with local and non-local boundary conditions. The dissertation divided into three chapters: In first chapter we have write the most important basic concepts, the theories, which had the strong relationship with the problems, discussed in others chapters, and which included the main result for this research and remarks about sobolev spaces H^k (Ω),H_0^k (Ω). In second chapter we discussed a solution of classical and generalized first boundary value problems with local boundary conditions . In third chapter we study the existence and uniqueness of the solution for Poisson equation with non-local first boundary condition, and discussed the existence and uniqueness of the solution of partial differential equation of elliptic as far as the previous conditions must be proved with the comparison principle. The argument of the proof for the previous problems depends on the following points shown below: Banach’s fixed point theorem in complete metric space. Maximum and minimum principle.In this dissertation we have to consider solution of linear and quasi-linear second order partial differential equations of elliptic type with local and non-local boundary conditions. The dissertation divided into three chapters: In first chapter we have write the most important basic concepts, the theories, which had the strong relationship with the problems, discussed in others chapters, and which included the main result for this research and remarks about sobolev spaces H^k (Ω),H_0^k (Ω). In second chapter we discussed a solution of classical and generalized first boundary value problems with local boundary conditions . In third chapter we study the existence and uniqueness of the solution for Poisson equation with non-local first boundary condition, and discussed the existence and uniqueness of the solution of partial differential equation of elliptic as far as the previous conditions must be proved with the comparison principle. The argument of the proof for the previous problems depends on the following points shown below: Banach’s fixed point theorem in complete metric space. Maximum and minimum principle.Local and non Local linear elliptic boundary value problems