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

Abstract EN

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.