In this study, we take under investigation principal functions corresponding to the eigenvalues and the spectral singularities of the Operator L generated in L2false(R+,Efalse) by the differential expression lfalse(yfalse)=−y′′+Qfalse(xfalse)y,3.0235ptx∈R+:=false[0,∞false) and the boundary condition (A0 + A1λ + A2λ2)y′(0,λ) − (B0 + B1λ + B2λ2)y(0,λ) = 0, where Q is a matrix‐valued function and Ai,Bi,i = 0,1,2 are non‐selfadjoint matrices also A2,B2 are invertible.

In this study, we consider the spectral analysis of the boundary value problem (BVP) consisting of the discrete Klein-Gordon equation and the quadratic eigenparameter-dependent boundary condition. Presenting the Jost solution and Green's function, we investigate the finiteness and other spectral properties of the eigenvalues and spectral singularities of this BVP under certain conditions.

In this study, we take under investigation principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) an−1yn−1 + bnyn + anyn+1 = λyn, n ∈ N and (γ0 + γ1λ) y1 + (β0 + β1λ) y0 = 0 where (an) and (bn) are complex sequences, λ is a hyperbolic eigenparameter and γi, βi ∈ C for i = 0, 1.

In this paper, we investigate a second order non-selfadjoint matrix Sturm-Liouville equation including a boundary condition that depends on quadratic eigenvalue parameter. Along with presenting a condition that ensures that this boundary value problem (BVP) has finitely many eigenvalues and spectral singularities with finite multiplicities, we have studied the point spectrum of this (BVP).

This paper is concerned with the boundary value problem (BVP) for the discrete Klein-Gordon equation a n−1 y n−1 + (v n − λ) 2 y n = 0, n ∈ N and the boundary condition γ 0 + γ 1 λ y 1 + β 0 + β 1 λ y 0 = 0 where (a n) , (v n) are complex sequences, γ i , β i ∈ C, i = 0, 1 and λ is a eigenparameter. The paper presents Jost solution, eigenvalues, spectral singularities and states some theorems concerning quantitative properties of the spectrum of this BVP under the condition n∈N exp n δ (|1 − a n | + |v n |) < ∞ for > 0 and 1 2 ≤ δ ≤ 1.