Bifurcation conditions for the solutions of weakly perturbed boundary-value problems for operator equations in Banach spaces

Abstract

We obtain bifurcation conditions for the solutions of weakly perturbed boundary-value problems for operator equations in Banach spaces from the point $\varepsilon = 0$. A convergent iterative procedure is proposed for the construction of solutions as parts of series in powers of $\varepsilon$ with pole at the point $\varepsilon = 0$.