Siberian Mathematical Journal

, Volume 51, Issue 4, pp 648–659 | Cite as

Completeness of elementary solutions to a class of second order operator-differential equations

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Abstract

We present conditions of solvability of a boundary value problem for a class of second order operator-differential equations on a finite segment, study the behavior of the resolvent of the corresponding operator pencil, prove the double completeness of a system of the derived chains of eigenvectors and associated vectors corresponding to a boundary value problem on a segment, and establish the completeness of elementary solutions to the homogeneous equation in the solution space.

Keywords

boundary value problem operator-differential equation Hilbert space selfadjoint operator eigenvectors and associated vectors resolvent 
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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Institute of Mathematics and Mechanics of the NAS of Azerbaijan and Baku State UniversityBakuAzerbaijan
  2. 2.Baku State UniversityBakuAzerbaijan

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