Geodesic
Implicit functions determined by equations with unbounded operators and the solvability of operator equations
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 216-224 Cet article a éte moissonné depuis la source Math-Net.Ru

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For implicit functions determined by the equation $Tx+F(\lambda,x)=0$, where $T$ is an unbounded operator, existence and differentiability conditions are established. Applications concerning the solvability conditions for equations of the form $Tx+f(x)=0$ are considered. 
@article{ZNSL_1998_248_a10,
     author = {M. N. Yakovlev},
     title = {Implicit functions determined by equations with unbounded operators and the solvability of operator equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {216--224},
     year = {1998},
     volume = {248},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a10/}
}
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M. N. Yakovlev. Implicit functions determined by equations with unbounded operators and the solvability of operator equations. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 216-224. http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a10/