R-holomorphic solutions and R-differentiable integrals of multidimensional differential systems

Details R-holomorphic solutions and R-differentiable integrals of multidimensional differential systems R-holomorphic solutions and R-differentiable integrals of multidimensional differential systems

2009-09-17

arxiv.org/abs/0909.3245v1

Mathematics

Dynamical Systems

29 pages

Scientific paper

We consider multidimensional differential systems (total differential systems and partial differential systems) with R-differentiable coefficients. We investigate the problem of the existence of R-holomorphic solutions, R-differentiable integrals, and last multipliers. The theorem of existence and uniqueness of R-holomorphic solution is proved. The necessary conditions and criteria for the existence of R-differentiable first integrals, partial integrals, and last multipliers are given. For a completely solvable total differential equation with R-holomorphic right hand side are constructed the classification of R-singular points of solutions and proved sufficient conditions that equation have no movable nonalgebraical R-singular points. The spectral method for building R-differentiable first integrals for linear homogeneous first-order partial differential systems with R-linear coefficients is developed.

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