zbMATH — the first resource for mathematics

Local solvability of differential equations in spaces of many-valued analytic functions. (English. Russian original) Zbl 0769.35002
Differ. Equations 27, No. 1, 82-91 (1991); translation from Differ. Uravn. 27, No. 1, 103-114 (1991).
The authors investigate the solutions of differential equations in the class of many valued analytic functions on complex manifolds. This theory was treated in detail by Yu. B. Sternin and V. E. Shatalov [Usp. Mat. Nauk 43, No. 3(261), 99–124 (1988; Zbl 0699.35031)] and in this paper the authors try to complete this work at least in the local case. The difficulties are mainly connected with the possible presence of interior or boundary strata in the set of singularities.
Reviewer: M.Biroli (Monza)
35A20 Analyticity in context of PDEs
58C10 Holomorphic maps on manifolds
32Q99 Complex manifolds
58J47 Propagation of singularities; initial value problems on manifolds