Generalized singular exponents linear system of differential equations
Keywords:
linear differential systems, singular exponents, nonlinear differential systems, stability, asymptotic stabilityAbstract
Consider a finite-dimensional linear homogeneous system of differential equations with continuous
bounded coefficients in an infinite interval in critical cases of singular exponents. We introduce
generalized singular upper and generalized singular lower exponents of the finite-dimensional linear
homogeneous system of differential equations with continuous and tending to zero coefficients in
an infinite interval. Formulas for calculating the generalized upper and generalized lower singular
exponents of the linear homogeneous system of differential equations with continuous and tending
to zero coefficients in an infinite interval were found. Introduced the asymptotic characteristics of
linear homogeneous systems of differential equations are used for researches of nonlinear systems
of differential equations. With the first approximation method investigated non-linear system of
differential equations and uniform upper bounds of solutions of nonlinear differential equations in
a defined class of nonlinear differential systems were established. We found sufficient conditions
for asymptotic stability of the zero solution of the nonlinear system of differential equations.
The generalized exponential stability of the zero solution of the nonlinear system of differential
equations was established.
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