Electron. J. Diff. Equ., Vol. 2013 (2013), No. 55, pp. 1-19.

Existence and stability of solutions to neutral equations with infinite delay

Xianlong Fu

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.

Show me the PDF file (283 KB), TEX file, and other files for this article.

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

Return to the EJDE web page