On global existence and attractivity results for nonlinear functional integral equations

✍ Scribed by Bapurao C. Dhage; V. Lakshmikantham

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 555 KB
• Volume: 72
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.10.021

✦ Synopsis

In this paper two existence results concerning the global attractivity and global asymptotic attractivity for a certain functional nonlinear integral equation are proved. Our existence results include several existence as well as attractivity results obtained earlier by Banas and Dhage (2008) [1], Hu and Yan (2006) [3], Dhage (2009) [15] and Banas and Rzepka (2003) [7] as special cases under some weaker Lipschitz conditions. A measure theoretic fixed point theorem of Dhage ( 2008) [6] is used in formulating our main results and the characterizations of solutions are obtained in the space of functions defined, continuous and bounded on unbounded intervals.