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

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.