Abstract:
One of directions in the development of Lomov's regularization method is the approach related to holomorphic regularization of singularly perturbed problems, which allows one to construct solutions to such problems in the form of series in powers of a small parameter converging in the usual sense. For boundary-value problems, the problem of pseudoholomorphic continuation of solutions is very urgent. In this paper, we examine a boundary-value problem for a Tikhonov system and give conditions for the existence of its pseudoholomorphic solution.