An automatic procedure for the calculation of bifurcation points of integral equations (Q1063414)

Let X,Y be Banach spaces, \(\lambda\), \(\mu\) real parameters, and \(F: X\to Y\) a mapping such that its Fréchet derivative F' at a singular point \((x^*,\lambda^*,\mu^*)\) of the nonlinear equation \(F(x,\lambda,\mu)=0\) is a Fredholm operator of index 0 and dim ker(F')\({}^*(x^*,\lambda^*,\mu^*)=1\). A new direct method for finding simple bifurcation points is presented.