Geodesic
On small solutions of nonlinear operator equations with noninvertible operator in the principal term
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 57-63

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In this paper, we examine a nonlinear operator equation with vector parameter, which does not satisfy the implicit operator theorem since the operator in the principal term is not continuously invertible at a given point. We prove a sufficient conditions of existing small continuous solution and propose an algorithm of constructing such solution in some domain.
Keywords: Banach space, nonlinear operator, operator equation, continuous solution, sectorial neighborhood of zero. 
@article{INTO_2022_212_a5,
     author = {R. Yu. Leontiev},
     title = {On small solutions of nonlinear operator equations with noninvertible operator in the principal term},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {57--63},
     publisher = {mathdoc},
     volume = {212},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_212_a5/}
}
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R. Yu. Leontiev. On small solutions of nonlinear operator equations with noninvertible operator in the principal term. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 212 (2022), pp. 57-63. http://geodesic.mathdoc.fr/item/INTO_2022_212_a5/