Principal functions of boundary-value problem with quadratic spectral parameter in boundary conditions

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 + a2λ2)y′(0) – (β0 + β1 λ + β2λ2)y(0) = 0, where q is a complex-valued function, αi, βi ∊ ℂ, i = 0,1,2 and λ is a eigenparameter, and introduce the convergence properties of principal functions.