The Maslov Index and Global Bifurcation for Nonlinear Boundary Value Problems

2012 ◽  
pp. 1-34
Author(s):  
Alberto Boscaggin ◽  
Anna Capietto ◽  
Walter Dambrosio
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Maslov Index ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

scholarly journals Global Bifurcation in2m-Order Generic Systems of Nonlinear Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Xiaoling Han ◽  
Jia Xu ◽  
Guowei Dai
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Solution Set ◽  
Nonlinear Boundary Value Problems ◽  
Countable Collection ◽  
Nonlinear Boundary Value

We consider the systems of(-1)mu(2m)=λu+λv+uf(t,u,v),  t∈(0,1),  u(2i)(0)=u(2i)(1)=0, and0≤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, whereλ,μ∈Rare real parameters.f,g:[0,1]×R2→RareCk,k≥3functions andf(t,0,0)=g(t,0,0)=0,t∈[0,1]. It will be shown that if the functions,fandgare “generic” then the solution set of the systems consists of a countable collection of 2-dimensional,Ckmanifolds.

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