Analysis of a bifurcation problem Original Research Article

It is about studying branches of bifurcation of a nonlinear equation of the type: u−λLu+g(λ,u,y)=0, in a neighborhood of a particular solution (λ0,0,0)∈R×E×F. E and F being two real Banach spaces, L a linear operator defines on E admitting λ0 for a characteristic value and g is a nonlinear operator defined on W to values in E. The bifurcation tempted several researchers by its different applications. Notably to the resolution of differential equations as those of Von–Karmann and Navier–Stokes or to integral equations as the Urysohn’s one (see ).