Geodesic
On local uniqueness of the solution of boundary-value problems
Matematičeskie zametki, Tome 15 (1974) no. 6, pp. 891-895.

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In this paper we present conditions under which differentiability of the mappings $F:AC^n(I)\to L^n(I)$ and $\Phi:AC^n(I)\to R^n$ at $x_0\in AC^n(I)$ and the uniqueness of the solution of the boundaryvalue problem $u'=F'(x_0)(u)$, $\Phi'(x_0)(u)=0$ imply local uniqueness of the solution $x_0$ of the boundary-value problem $x'=F(x)$, $\Phi(x)=0$. 
@article{MZM_1974_15_6_a7,
     author = {V. D. Ponomarev},
     title = {On local uniqueness of the solution of boundary-value problems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {891--895},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_6_a7/}
}
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V. D. Ponomarev. On local uniqueness of the solution of boundary-value problems. Matematičeskie zametki, Tome 15 (1974) no. 6, pp. 891-895. http://geodesic.mathdoc.fr/item/MZM_1974_15_6_a7/