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<p>Analytic properties of solutions of differential equations with a small parameter form the basis of the analytic perturbation theory. In the case of a regular theory, Poincaré decomposition theorems or statements that follow from the concept of an analytic family in the sense of Kato hold. For singularly perturbed problems, the approach based on S.&#xa0;A.&#xa0;Lomov’s regularization method is useful; the central concept of this method is the concept of pseudo-analytic (pseudo-holomorphic) solutions, i.e., solutions that can be represented in the form of series in powers of a small parameter converging in the usual sense.</p>

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SMOOTHNESS IN THE VISCOSITY OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS IN A BANACH SPACE

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • V. I. Kachalov

摘要

Analytic properties of solutions of differential equations with a small parameter form the basis of the analytic perturbation theory. In the case of a regular theory, Poincaré decomposition theorems or statements that follow from the concept of an analytic family in the sense of Kato hold. For singularly perturbed problems, the approach based on S. A. Lomov’s regularization method is useful; the central concept of this method is the concept of pseudo-analytic (pseudo-holomorphic) solutions, i.e., solutions that can be represented in the form of series in powers of a small parameter converging in the usual sense.