×

Existence results for semilinear neutral functional differential equations involving evolution operators in Fréchet spaces. (English) Zbl 1210.34109

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.

MSC:

34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations
47N20 Applications of operator theory to differential and integral equations
PDFBibTeX XMLCite
Full Text: DOI