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. 
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/
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