Well-posedness of conditionally correct integro-differential equations in new pair of non-weighted Sobolev spaces

In this paper we investigate the general boundary-value problem for linear integro-differential equations, specified on a segment of the number line where the order of the internal differential operators is of higher order than that of the corresponding exterior differential operator. We prove well-posedness of this problem in the Hadamard sense in new pair of non-weighted Sobolev spaces.