Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 55, pp. 1-19.

Title: Existence and stability of solutions to neutral
       equations with infinite delay
        
Author: Xianlong Fu (East China Normal Univ., Shanghai, China)

Abstract:
 In this article, 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.


Submitted September 16, 2012. Published February 21, 2013.
Math Subject Classifications: 34K25, 34K30, 34G20.
Key Words: Neutral functional differential equation; analytic semigroup;
           fractional power operator; linearized stability;
           infinite delay.