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Статья
2018

On Analytic Periodic Solutions to Nonlinear Differential Equations With Delay (Advance)


A. A. KosovA. A. Kosov, E. I. SemenovE. I. Semenov
Русская математика
https://doi.org/10.3103/S1066369X18100043
Abstract / Full Text

We study a system of the reaction–diffusion type, where diffusion coefficients depend in an arbitrary way on spatial variables and concentrations, while reactions are expressed as homogeneous functions whose coefficients depend in a special way on spatial variables. We prove that the system has a family of exact solutions that are expressed through solutions to a system of ordinary differential equations (ODE) with homogeneous functions in right-hand sides. For a special case of theODE systemwe construct a general solution represented by Jacobi higher transcendental functions. We also prove that these periodic solutions are analytic functions that can be expressed near each point on the period by convergent power series.

Author information
  • Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, RussiaA. A. Kosov & E. I. Semenov
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