On a boundary value problem with shift for an equation of mixed type in an unbounded domain
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- Repin, O.A. & Kumykova, S.K. Diff Equat (2012) 48: 1127. doi:10.1134/S0012266112080083
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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.