Weakly Perturbed Fredholm Integral Equations with Degenerate Kernels in Banach Spaces

We consider weakly perturbed Fredholm equations with degenerate kernels in Banach spaces and establish conditions for ε = 0 to be a bifurcation point for the solutions of weakly perturbed operator equations X in Banach spaces. A convergent iterative scheme for finding solutions in the form of series Σi=−1+∞εizi(t) in powers of ε is proposed. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.