Smoothness in the viscosity of solutions of nonlinear differential equations in a Banach space

The analytical properties of solutions of differential equations with a small parameter form the basis of analytical perturbation theory. In the case of a regular theory, Poincaré's 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 a pseudoanalytic (pseudoholomorphic) solution, i.e., a solution, which can be represented in the form of a series converging in the usual sense in powers of a small parameter.