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

被引：2

作者：

Bikchantaev I.A. ^{[1
]}

机构：

[1] N.I. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Kremlevskaya ul. 18, Kazan, Tatarstan

来源：

Lobachevskii Journal of Mathematics | 2018年 / 39卷 / 2期

关键词：

boundary value problem; defect number; elliptic equation; index; periodic solution;

D O I：

10.1134/S199508021802004X

中图分类号：

学科分类号：

摘要：

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. © 2018, Pleiades Publishing, Ltd.

引用

页码：165 / 168

页数：3

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