Electron. J. Diff. Equ., Vol. 2013 (2013), No. 219, pp. 1-13.

Third-order operator-differential equations with discontinuous coefficients and operators in the boundary conditions

Araz R. Aliev, Nazila L. Muradova

Abstract:
We study a third-order operator-differential equation on the semi-axis with a discontinuous coefficient and boundary conditions which include an abstract linear operator. Sufficient conditions for the well-posed and unique solvability are found by means of properties of the operator coefficients in a Sobolev-type space.

Submitted June 7, 2013. Published October 4, 2013.
Math Subject Classifications: 47E05, 34B40, 34G10.
Key Words: Operator-differential equation; discontinuous coefficient; operator-valued boundary condition; self-adjoint operator; regular solvability; Sobolev-type space; intermediate derivative operators.

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Araz R. Aliev
Baku State University
Institute of Mathematics and Mechanics of NAS of Azerbaijan
Baku, Azerbaijan
email: alievaraz@yahoo.com
Nazila L. Muradova
Nakhchivan State University
Nakhchivan, Azerbaijan
email: nazilamuradova@gmail.com

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