PRINCIPAL FUNCTIONS OF BOUNDARY-VALUE PROBLEM WITH QUADRATIC SPECTRAL PARAMETER IN BOUNDARY CONDITION

Authors : Nihal Yokuş, Turhan Köprübaşı

Pages : 371-379

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Publication Date : 2017-03-14

Article Type : Other Papers

Abstract :In this paper, we determine the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem insert ignore into journalissuearticles values(BVP); -y′′+qinsert ignore into journalissuearticles values(x);y=λ²y, x∈ℝ₊=[0,∞] insert ignore into journalissuearticles values(α₀+α₁λ+α₂λ²);y′insert ignore into journalissuearticles values(0);-insert ignore into journalissuearticles values(β₀+β₁λ+β₂λ²);yinsert ignore into journalissuearticles values(0);=0, where q is a complex-valued function, α_{i}, β_{i}∈ℂ, i=0,1,2 and λ is a eigenparameter, and introduce the convergence properties of principal functions.
Keywords : Eigenvalue, Jost solution, principal function, non selfadjoint differential operator, spectral analysis, spectral singularity