The uniform lower bound of solutions of nonlinear system of differential equations

  • Zh. Т. Moldabek Казахский национальный университет имени аль-Фараби, Республика Казахстан, Алматы
  • T. М. Aldibekov Казахский национальный университет имени аль-Фараби, Республика Казахстан, Алматы

Abstract

We study non-linear system of differential equations in finite-dimensional vector space with the method of the first approximation. A system of the first approximation were considered, i.e. a linear system of differential equations with continuous and tending to zero coefficients on infinite interval. Singular exponents of a linear system of differential equations, in this case taking the critical ie, zero values, so are unsuitable for use. The paper defined the generalized special lower rate of a linear system of differential equations with continuous and tending to zero coefficients. We present an equivalent definition of a generalized special low index of a linear system of differential equations with continuous and tending to zero coefficients. Applying a generalized lower specific indicator of a linear system of differential equations with continuous and tending to zero coefficients obtained uniform lower estimate of solutions of differential equations solving the nonlinear system in a certain class of nonlinear differential systems. Powered sufficient condition for the instability of the zero solution of nonlinear differential equations.

References

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Published
2018-07-18
How to Cite
MOLDABEK, Zh. Т.; ALDIBEKOV, T. М.. The uniform lower bound of solutions of nonlinear system of differential equations. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 92, n. 4, p. 46-54, july 2018. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/453>. Date accessed: 10 dec. 2018.
Keywords linear differential systems, singular exponents, nonlinear differential systems, bound of the solutions