On implicit abstract neutral nonlinear differential equations

Abstract

In this paper we continue our developments in Hernández and O'Regan (J Funct Anal 261:3457-3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O'Regan (J Funct Anal 261:3457-3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial "nonlinear" neutral differential equations. Some applications involving partial neutral differential equations are presented.