Explicit criteria for the existence of positive solutions for a scalar differential equation with variable delay in the critical case

✍ Scribed by Josef Diblík; Zdeněk Svoboda; Zdeněk Šmarda

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 266 KB
• Volume: 56
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2008.01.015

✦ Synopsis

A scalar linear differential equation with time-dependent delay ẋ

The goal of our investigation is to give sufficient conditions for the existence of positive solutions as t → ∞ in the critical case in terms of inequalities on a and τ . A generalization of one known final (in a certain sense) result is given for the case of τ being not a constant. Analysing this generalization, we show, e.g., that it differs from the original statement with a constant delay since it does not give the best possible result. This is demonstrated on a suitable example.