Periodic solutions for a class of neutral functional differential equations with infinite delay

✍ Scribed by Guirong Liu; Weiping Yan; Jurang Yan

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 648 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.10.096

✦ Synopsis

In this paper, we study the existence and uniqueness of periodic solutions of the nonlinear neutral functional differential equation with infinite delay of the form d dt

In the process we use the fundamental matrix solution of

and construct appropriate mappings, where u ∈ C (R, R n ) is an ω-periodic function. Then we employ matrix measure and the Leray-Schauder fixed point theorem to show the existence of periodic solutions of this neutral differential equation. In the special case where g(s, u) ≡ 0 and A(t, x) = A(t), some sufficient conditions which ensure the uniform stability and global attractivity of a unique periodic solution are derived.