Baghli, Selma; Benchohra, Mouffak Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces. (English) Zbl 1210.34109 Georgian Math. J. 17, No. 3, 423-436 (2010). The authors establish the existence and uniqueness of mild solutions to a class of abstract first-order time-dependent neutral functional differential equations on a semi-infinite interval. A key tool in the approach is a Leray-Schauder type alternative for contraction maps in Fréchet spaces. The study is extended to the case of neutral evolution equations with nonlocal conditions. Reviewer: Sergiu Aizicovici (Athens/Ohio) Cited in 13 Documents MSC: 34K30 Functional-differential equations in abstract spaces 34K40 Neutral functional-differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:functional differential equation; evolution operators; mild solution PDFBibTeX XMLCite \textit{S. Baghli} and \textit{M. Benchohra}, Georgian Math. J. 17, No. 3, 423--436 (2010; Zbl 1210.34109) Full Text: DOI