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Gradient Structures Associated with a Polynomial Differential Equation

Author

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in R n is described by solving the Cauchy Problem for the corresponding first order system of PDEs. Moreover, the kernel representation has a special significance on the space of solutions to the corresponding system of PDEs. As very important applications, it has been established that the mathematical framework developed in this work can be used for the study of some second-order PDEs involving a finite set of derivations.

Suggested Citation

  • Savin Treanţă, 2020. "Gradient Structures Associated with a Polynomial Differential Equation," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:535-:d:341562
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    Citations

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    Cited by:

    1. Beny Neta, 2021. "A New Derivative-Free Method to Solve Nonlinear Equations," Mathematics, MDPI, vol. 9(6), pages 1-5, March.
    2. Michal Fečkan & Július Pačuta, 2020. "Averaging Methods for Second-Order Differential Equations and Their Application for Impact Systems," Mathematics, MDPI, vol. 8(6), pages 1-11, June.

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