Fu, Xianlong Existence and stability of solutions to neutral equations with infinite delay. (English) Zbl 1293.34103 Electron. J. Differ. Equ. 2013, Paper No. 55, 19 p. (2013). Summary: By using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and alpha-norm is used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. A stability result for the autonomous case is also established. We conclude with an example that illustrates the applications of the results obtained. Cited in 3 Documents MSC: 34K40 Neutral functional-differential equations 34K25 Asymptotic theory of functional-differential equations 34K30 Functional-differential equations in abstract spaces 34K20 Stability theory of functional-differential equations Keywords:neutral functional differential equation; analytic semigroup; fractional power operator; linearized stability; infinite delay PDFBibTeX XMLCite \textit{X. Fu}, Electron. J. Differ. Equ. 2013, Paper No. 55, 19 p. (2013; Zbl 1293.34103) Full Text: EMIS