×

Existence and stability of solutions to neutral equations with infinite delay. (English) Zbl 1293.34103

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.

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
PDFBibTeX XMLCite
Full Text: EMIS