Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems. (18th December 2012)

• Record Type: Journal Article
• Authors: Han, Xiaoling; Xu, Jia; Dai, Guowei
• Other Names: Li Chuandong Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-12-18
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/804619
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider the systems of ( - 1 ) m u ( 2 m ) = λ u + λ v + u f ( t, u, v ), t ∈ ( 0, 1 ), u ( 2 i ) ( 0 ) = u ( 2 i ) ( 1 ) = 0, and 0 ≤ i ≤ m - 1, ( - 1 ) m v ( 2 m ) = μ u + μ v + v g ( t, u, v ), t ∈ ( 0, 1 ), v ( 2 i ) ( 0 ) = v ( 2 i ) ( 1 ) = 0, 0 ≤ i ≤ m - 1, where λ, μ ∈ R are real parameters. f, g : [ 0, 1 ] × R 2 → R are C k, k ≥ 3 functions and f ( t, 0, 0 ) = g ( t, 0, 0 ) = 0, t ∈ [ 0, 1 ] . It will be shown that if the functions, f and g are "generic" then the solution set of the systems consists of a countable collection of 2-dimensional, C k manifolds.