Global bifurcation theorem for a class of boundary conditions for ordinary differential equations of second order

✍ Scribed by Jacek Gulgowski

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 138 KB
• Volume: 278
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310248

✦ Synopsis

Abstract

In this paper we deal with boundary value problems

equation image

where l : C^1^([a, b], ℝ^k^) → ℝ^k^ × ℝ^k^ is continuous, μ ≤ 0 and φ is a Caratheodory map. We define the class S of maps l, for which a global bifurcation theorem holds for the problem (+), with φ(t, x, y, λ) = λ(|x~1~|, …, |x^k^|) + o(|x| + |y|). We show that the class S contains Sturm‐Liouville boundary conditions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)