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

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.