Abstract
We consider the nonlinear equation B(λ)x = R(x, λ) + b(λ), where R(0, 0) = 0, b(0) = 0, the linear operator B(λ) has a bounded inverse operator for S ∋ λ → 0, and S is an open set, 0 ∈ ∂S. We examine the existence of a small continuous solution of the maximal order of smallness x(λ) → 0 as S ∋ λ → 0. A constructive method of constructing this solution is presented.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 183, Differential Equations and Optimal Control, 2020.
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Leontyev, R.Y. Minimal Branches of Solutions of Nonlinear Operator Equations in Banach Spaces. J Math Sci 279, 684–690 (2024). https://doi.org/10.1007/s10958-024-07051-x
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DOI: https://doi.org/10.1007/s10958-024-07051-x