On local uniqueness of the solution of boundary-value problems

In this paper we present conditions under which differentiability of the mappings F: ACⁿ(I) Lⁿ(I) and :ACⁿ(I) Rⁿ at x₀ ACⁿ(I) and the uniqueness of the solution of the boundaryvalue problem u = F(x₀)(u), (x₀)(u) = 0 imply local uniqueness of the solution x₀ of the boundary-value problem x = F(x), (x) = 0.Translated from Matematicheskie Zametki, Vol. 15, No. 6, pp. 891–895, June, 1974.The author thanks A. Ya. Lepin for the help he has given him in the preparation of this paper.