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

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.

Keywords

• Operator-differential equation
• discontinuous coefficient
• operator-valued boundary condition
• self-adjoint operator
• regular solvability
• Sobolev-type space
• intermediate derivative operators