Global Bifurcation in 2m‐Order Generic Systems of Nonlinear Boundary Value Problems

Xiaoling Han, Jia Xu and Guowei Dai

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We consider the systems of (−1) mu(2m) = λu + λv + uf(t, u, v), t ∈ (0,1), u(2i)(0) = u(2i)(1) = 0, and 0 ≤ i ≤ m − 1, (−1) mv(2m) = μu + μv + vg(t, u, v), t ∈ (0,1), v(2i)(0) = v(2i)(1) = 0, 0 ≤ i ≤ m − 1, where λ, μ ∈ R are real parameters. f, g : [0,1] × R2 → R are Ck, 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, Ck manifolds.

Date: 2012
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https://doi.org/10.1155/2012/804619

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:804619

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