A partial functional differential equation of Sobolev type

Abstract

where r(t), t > 0 is the semigroup of bounded linear operators generated by -AB-‘. Equations of type (1.1) have been considered by several authors [24; g-101. In particular our motivation comes from the recent article of Brill [2]. The method employed here is different from Brill’s; however, our results reduce to his when r = 0. The article [ 111 contains results on partial functional differential equations when B = I. Equation (1.1) can be considered as an abstraction of the partial functional differential equation