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References (8)
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V. Kachalov (2019)
Poincare decomposition theorems and the Lomov regularization methodJournal of Physics: Conference Series, 1391
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A. Bobodzhanov, V. Safonov, V. Kachalov (2019)
Asymptotic and Pseudoholomorphic Solutions of Singularly Perturbed Differential and Integral Equations in the Lomov's Regularization MethodAxioms, 8
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On a nonlinear differential equation in a Banach spaceSibirskie Elektronnye Matematicheskie Izvestiya
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Pseudo-analytic solutions of singularly perturbed problemsDokl. Math., 49
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2022
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/s0012266122030065
- Publisher site
- See Article on Publisher Site
Abstract
For nonlinear evolution equations in a Banach space that depend in twoways—regularly and singularly—on a small parameter, we construct\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varepsilon$$\end{document}-pseudoregular solutions of the Cauchy problem,i.e., its formal solutions representable as series in powers of the small parameter with coefficientsthat depend on it in a singular way and converging in a certain neighborhood of the zero value ofthe parameter uniformly over a given time interval. Sufficient conditions are obtained under whichthe sum of such a series is an exact, and hence pseudoholomorphic, solution of this problem.
Journal
Differential Equations – Springer Journals
Published: Mar 1, 2022