Tamaz Tadumadze and Nika Gorgodze
abstract:
For the quasi-linear neutral functional differential equation the continuous
dependence of a solution of the Cauchy problem on the initial data and on the
nonlinear term in the right-hand side of that equation is investigated, where
the perturbation nonlinear term in the right-hand side and initial data are
small in the integral and standard sense, respectively. Variation formulas of a
solution are derived, in which the effect of perturbations of the initial moment
and the delay function, and also that of the discontinuous initial condition are
detected. For initial data optimization problems the necessary conditions of
optimality are
obtained. The existence theorem for optimal initial data is proved.
Mathematics Subject Classification: 34K38, 34K40, 34K27, 49J21, 49K21
Key words and phrases: Quasi-linear neutral functional differential equation, continuous dependence of solution, variation formula of solution, effect of initial moment perturbation, effect of a discontinuous initial condition, effect of delay function perturbation, initial data optimization problem, necessary conditions of optimality, existence of optimal initial data