Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 165–168 | Cite as

Periodic Conjugation Problem for Linear Elliptic Equations of Second Order with Constant Coefficients

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Abstract

We consider a periodic problem of conjugation on the real axis for a linear differential elliptic equation of second order with constant coefficients. There is known a representation of general solution of the equation in terms of analytic functions depending on affine connected variables. We introduce auxiliary analytic functions enabling us to reduce the problem to a system of two periodic Riemann boundary value problems. That problem was solved first by L. I. Chibrikova. We use her results for solving of our problem. We obtain its explicit solution and conditions of solvability, evaluate the index and defect numbers.

Keywords and phrases

elliptic equation boundary value problem defect number index periodic solution 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.N.I. Lobachevskii Institute of Mathematics and MechanicsKazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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