(1) Department of Mathematics and Statistics, Indian Institute of Technology Kanpur
Kanpur, Uttar Pradesh, INDIA, Pin-208016
(2) Department of Mathematics, Indian Institute of Technology Roorkee
Uttarakhand, INDIA, Pin-247667
Received June 15, 2011
Accepted September 15, 2011
Communicated by Joël Blot
Abstract. We study the existence, uniqueness and asymptotic stability of solutions to a neutral differential equation with a deviated argument in an arbitrary Banach space. The results are obtained by applying the Sobolevskiĭ-Tanabe theory of parabolic equations, fractional powers of operators and the Banach fixed point theorem. As an application, we include an example to illustrate the theory. | |
2010 Mathematics Subject Classification: 34G20, 34K30, 34K40, 47N20. |
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