Generalized Solutions

Abstract

The following classes of weak solutions of hyperbolic functional differential problems are considered in literature. Mixed problems for almost linear systems in two independent variables were considered in [167], see also [102]. A continuous function is a solution of a mixed problem if it satisfies integral functional system arising from functional differential system by integrating along bicharacteristics. The paper [167] initiated investigations of first order functional differential equations. Existence theorems and differential inequalities generated by almost linear functional differential problems can be found in [42, 107, 123]. Distributional solutions of almost linear problems were considered in [204]. The method used in this paper is constructive, it is based on a difference scheme. Barbashin type functional differential problems are discussed in [102].