Non-Selfadjoint Matrix Sturm-Liouville Operators with Eigenvalue-Dependent Boundary Conditions

Abstract

In this paper we investigate discrete spectrum of the non-selfadjoint matrix Sturm-Liouville operator L generated in L (R+, S) by the differential expression ` (y) = −y +Q (x) y , x ∈ R+ : [0,∞) , and the boundary condition y′ (0)− ( β0 + β1λ+ β2λ 2 ) y (0) = 0 where Q is a non-selfadjoint matrix valued function. Also using the uniqueness theorem of analytic functions we prove that L has a finite number of eigenvalues and spectral singularities with finite multiplicities. 2000 AMS Classification: 34B24, 34L40 , 47A10.