FUNCTIONAL HAMILTON-JACOBI TYPE EQUATIONS IN CI-DERIVATIVES FOR SYSTEMS WITH DISTRIBUTED DELAYS

Abstract

The paper develops the theory of generalized minimax solutions for the new class of functional Hamilton-Jacobi type equations withco-invariant derivatives which arise in extremal problems of dynamics with aftereffect. Various definitions (non-local and infinitesimal) of the minimax solution to such an equation are given, their equivalence is proved, and the existence and uniqueness results are obtained.