The number of bifurcation points of a periodic one-parameter ODE with at most two periodic solutions

✍ Scribed by José L. Bravo; Manuel Fernández; Antonio Tineo

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 295 KB
• Volume: 57
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2004.01.002

✦ Synopsis

We study the number of bifurcation points of x = F(t; x; ), where F is periodic in t, continuous, and locally Lipschitz continuous with respect to x, by assuming that the di erential equation has at most two periodic solutions for each ∈ R. Under some additional assumptions we prove that there are at most two bifurcation points and we ÿnd su cient conditions under which this equation has exactly k bifurcation values, where k = 0; 1; 2.