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

Year 2017, Volume: 30 Issue: 1, 371 - 379, 14.03.2017

Nihal Yokuş , Turhan Köprübaşı

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.

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