Asymptotic solutions of eigenfunctions and Green's functions for regular Sturm-Liouville problems having eigenvalue parameter in the boundary condition

In this thesis, eigenfunctions of the second order regular Sturm-Liouville problems have been investigated for different boundary conditions in case where the potential function is integrable and differentiable seperately. First, asymptotic solutions for eigenfunctions for the cases where the right-hand boundary condition is constant and the left-hand boundary condition contains affine λ-dependent(A), bilinear λ-dependent(B) or quadratic λ-dependent(K) function have been obtained seperately. Then, asymptotic solutions for eigenfunctions in case where both boundary conditions depend on the eigenvalue parameter have been found. Finally, asymptotic approximations for Green's functions using the derived results for eigenfunctions have been evaluated.