A Variational Approach towards Solving an Ill-Posed Cauchy Problem for a Functional-Differential Equation

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.