Well-posed integro-differential equations in a new pair of weight-free Sobolev spaces

Abstract

© 2017, Allerton Press, Inc. We are dealing with general boundary-value problem for linear integro-differential equations on a segment of the real axis. In the case under consideration the order of internal differential operators is higher than the order of exterior one. We prove that the problem is wellposed in the Hadamard sense in a new pair of weight-free Sobolev spaces.