On a boundary value problem with shift for an equation of mixed type in an unbounded domain
- First Online:
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.
Unable to display preview. Download preview PDF.
- 5.Tricomi, F., Lezioni sulle equazioni a derivate parziali, Turin, 1954. Translated under the title Lektsii po uravneniyam v chastnykh proizvodnykh, Moscow: Inostrannaya literatura, 1957.Google Scholar
- 6.Bitsadze, A.V., Nekotorye klassy uravnenii v chastnykh proizvodnykh (Some Classes of Partial Differential Equations), Moscow: Nauka, 1981.Google Scholar
- 7.Lebedev, N.N., Spetsial’nye funktsii i ikh prilozheniya (Special Functions and Their Applications), Moscow: Gosudarstv. Izdat. Fiz.-Mat. Lit., 1963.Google Scholar
- 10.Smirnov, M.M., Uravneniya smeshannogo tipa (Equations of Mixed Type), Moscow: Vyssh. Shkola, 1985.Google Scholar