A variational approach towards solving an ill-posed cauchy problem for a functional-differential equation

Abstract

We investigate an ill-posed Cauchy problem for a linear functional differential equation of retarded type on the negative half-line. Using a step-by-step procedure this problem is replaced by an inverse problem for an operator equation of the first kind in a functional space. The Tikhonov’s method is then used for finding solutions. We also construct special boundary value problems for the functional differential equations. Solutions of these boundary value problems determine regularized solutions of the ill-posed Cauchy problem by the step-by-step procedure. © 2016, DEStech Publications Inc. All rights reserved.