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Global bifurcation theorem for a class of boundary conditions for ordinary differential equations of second order
Author(s) -
Gulgowski Jacek
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310248
Subject(s) - mathematics , bifurcation , class (philosophy) , ordinary differential equation , order (exchange) , boundary value problem , image (mathematics) , mathematical analysis , boundary (topology) , pure mathematics , differential equation , discrete mathematics , nonlinear system , physics , finance , quantum mechanics , artificial intelligence , computer science , economics
In this paper we deal with boundary value problemswhere 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)