On the uniqueness of solutions of neutral functional differential equations

Abstract

By applying differential inequalities, Lakshmikantham and Leela obtained general uniqueness results of Kamke’s form for retarded functional differential equations in their work [ 11. For general neutral functional differential equations, we have only a Lipschitzian uniqueness theorem which was obtained by Hale [2,3]. No one has established a uniqueness result of Kamke’s form in general NFDEs up to now, because it is difficult to establish proper differential inequalities. By using a special technique of “quasidistance,” the author gave a uniqueness theorem of Kamke’s form for the special NFDEs