Partial Differential Equations

Differential Equations

, Volume 48, Issue 8, pp 1127-1136

First online:

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

  • O. A. RepinAffiliated withSamara State Economic UniversityKabardino-Balkar State University
  • , S. K. KumykovaAffiliated withSamara State Economic UniversityKabardino-Balkar State University

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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.