Differential Equations

, Volume 48, Issue 8, pp 1127–1136

On a boundary value problem with shift for an equation of mixed type in an unbounded domain

  • O. A. Repin
  • S. K. Kumykova
Partial Differential Equations

DOI: 10.1134/S0012266112080083

Cite this article as:
Repin, O.A. & Kumykova, S.K. Diff Equat (2012) 48: 1127. doi:10.1134/S0012266112080083

Abstract

We study the unique solvability of a problem with shift for an equation of mixed type in an unbounded domain. We prove the uniqueness theorem under inequality-type constraints for known functions for various orders of the fractional differentiation operators in the boundary condition. The existence of a solution is proved by reduction to a Fredholm equation of the second kind, whose unconditional solvability follows from the uniqueness of the solution of the problem.

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • O. A. Repin
    • 1
    • 2
  • S. K. Kumykova
    • 1
    • 2
  1. 1.Samara State Economic UniversitySamaraRussia
  2. 2.Kabardino-Balkar State UniversityNalchikRussia