Weakly Perturbed Fredholm Integral Equations with Degenerate Kernels in Banach Spaces

Abstract

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 \( {\Sigma}_{i=-1}^{+\infty }{\varepsilon}^i{z}_i(t) \) in powers of ε is proposed.