We obtain the conditions of bifurcation of the solutions of weakly perturbed operator equations in Banach spaces from the
point $\varepsilon = 0$ and propose a convergent iterative procedure for finding the solutions in the form of parts of the series in
powers of $\varepsilon$ with pole at the point $\varepsilon = 0$.
Citation Example:Zhuravlev V. F. Weakly perturbed operator equations in Banach spaces // Ukr. Mat. Zh. - 2017. - 69, № 6. - pp. 751-764.