Baghli, Selma; Benchohra, Mouffak Perturbed functional and neutral functional evolution equations with infinite delay in Fréchet spaces. (English) Zbl 1190.34098 Electron. J. Differ. Equ. 2008, Paper No. 69, 19 p. (2008). The authors consider evolution equations of the form: \[ \begin{aligned} &\frac {d}{dt}[y(t) - h(t, y_t )] = A(t)y(t) + f (t, y_t ) + g(t, y_t ),\quad t \in J : = [0,\infty)\\ & y_0 = \phi \in B,\end{aligned} \]where \(f,g,h\) and \(\phi\) are given functions, \(B\) is the phase space and \(\{A(t)\}\) is a family of linear closed operators from a real Banach space \((E, | . | )\) into \(E\) that generates an evolution system of operators.Sufficient conditions for the existence of mild solutions on the positive half-line are obtained. As main tools the nonlinear alternative proved by Avramescu and the semigroup theory are used. Two examples which illustrate the results are given. Reviewer: Miklavž Mastinšek (Maribor) Cited in 11 Documents MSC: 34K30 Functional-differential equations in abstract spaces 34K40 Neutral functional-differential equations Keywords:perturbed functional and neutral functional evolution equation PDFBibTeX XMLCite \textit{S. Baghli} and \textit{M. Benchohra}, Electron. J. Differ. Equ. 2008, Paper No. 69, 19 p. (2008; Zbl 1190.34098) Full Text: EuDML EMIS