M.Sc. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: This thesis is composed of two parts. In the first part, we give some basic theory related to regular Sturm-Liouville problem including the differential equation Ly(x) ∶= a0(x)y′′(x) + a1(x) y′(x) + a2(x)with non-seperated boundary conditions a11y(a) + a12y ′(a) + b11y(b) + b12 y ′(b) = 0a21y(a) + a22y ′(a) + b21y(b) + b22 y ′(b) = 0. In the second part, we first prove some theoretical resullts for eigenvalue problems including self-adjointness, simple eigenvalues, green’s function and obtaining Δ discriminant function and then some asymptotic estimates for the eigenvalues of the boundary value problem including the differential equationy′′ (x) + (λ−q(x))y(x) = 0 , x ∈ [a,b] with seperated boundary conditionsa0 y(a) + a1y′(a) = 0 b0 y(b) + b1y′(b) = 0are obtained. The error term o(n−3) which appears in the asymptotic estimates of the eigenvalues in [3] is improved to o(n−4) in our same type of results. Key Words: Regular Sturm-Liouville problems, Eigenvalues, Asymptotic estimates | |||||||||||||||||||||