The green's function of regular boundary value problem

This study basically consists of three sections. In the first section, we formulate Green's functions for boundary value problems based on some main theory. In the second section, e consider the boundary value problem y^''+(λ-q)y=0 ,0≤x≤π (y^'(0,λ))/(y(0,λ))=-tanα, cosβy^'(π,λ)+sinβy(π,λ)=0 and compute Green's functions associuted with it. In addition to these, we also consider Dirichlet and Neumann boundary conditions. In the last section, we particularly consider the special integrable potential q(x)=x^(-1⁄2)-2/√π, and find asymptotic estimates for the solutions satisfying certain initial values, and then using these estimates we evaluate Green's functions.