Study of singularities in partial differential equations

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1. Nonlinear totally characteristic type partial differential equations were studied in the complex domain and the following results were obtained :(1) Unique existence result of the holomorphic solution was proved under Poincare condition and non-resonance condition.(2) The solvability was proved also in the case where non resonance condition is not satisfied.2. Solutions with singularities on a hypersurface were studied in linear and nonlinear partial differential equations and the following results were obtained :(1) Solvability of a particular class of linear partial differential equations Puf was proved in the space of functions with regular singularities.(2) By using the integral representation of homogeneous solutions, the asymptotic behavior was determined.(3) Branching of singularities was studied in linear Fuchsian partial differential equations.(4) Non-existence of a class of singularities was proved in nonlinear Fuchsian partial differential equations.3. The possibility of the analytic continuation of holomorphic solutions to nonlinear partial differential equations was studied and the non-existence of some class of singularities was proved.4. A class of p-elliptic differential equations was studied and the structure of regular singularities was determined.