Convergence of solutions for two delays Volterra integral equations in the critical case

✍ Scribed by Eleonora Messina; Yoshiaki Muroya; Elvira Russo; Antonia Vecchio

• Book ID: 104000913
• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 254 KB
• Volume: 23
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.05.002

✦ Synopsis

In this paper, for the ''critical case'' with two delays, we establish two relations between any two solutions y(t) and y * (t) for the Volterra integral equation of non-convolution type y(t) = f (t)+ t-δ t-τ k(t, s)g(y(s))ds and a solution z(t) of the first order differential equation

and offer a sufficient condition that lim t→+∞ (y(t)y * (t)) = 0.