Applicability of the linearization method for calculating the bifurcation points of a class of operator equations (Q1593951)

This article deals with the bifurcation problem \[ Lx= F(x, \lambda), \] where \(L\) is a Fredholm linear operator with dense domain and with nontrivial kernel and cokernel between Banach spaces \(E_1\) and \(E_2\), \(F: E_1\times \mathbb{R}\to E_2\) \((F(0,\lambda)= 0)\) is a nonlinear operator Fréchet differentiable at \(x= 0\). The authors present some theorems about bifurcation points in terms of a priori estimates of special kind.