Xianlong Fu
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.
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Xianlong Fu Department of Mathematics East China Normal University Shanghai, 200241, China email: xlfu@math.ecnu.edu.cn |
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