WEAKLY PERTURBED BOUNDARY-VALUE PROBLEMS FOR THE FREDHOLM INTEGRAL EQUATIONS WITH DEGENERATE KERNEL IN BANACH SPACES

摘要

We consider weakly perturbed boundary-value problems for the Fredholm integral equations with degenerate kernel in Banach spaces and establish the conditions of bifurcation from the point s = 0 for the solutions of weakly perturbed boundary-value problems for Fredholm integral equations with degenerate kernel in Banach spaces. A convergent iterative procedure is proposed for finding the solutions in the form of series ∑_(i=-1)~(+∞) ε~i z_i (t) in powers of s.