- Gazi University Journal of Science
- Vol: 30 Issue: 1
- PRINCIPAL FUNCTIONS OF BOUNDARY-VALUE PROBLEM WITH QUADRATIC SPECTRAL PARAMETER IN BOUNDARY CONDITIO...
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
Abstract :In this paper, we determine the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) -y′′+q(x)y=λ²y, x∈ℝ₊=[0,∞] (α₀+α₁λ+α₂λ²)y′(0)-(β₀+β₁λ+β₂λ²)y(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.