Estimates for solutions of linear and quasilinear systems in the nonautonomous case

Abstract

By using the freezing method, we obtain upper and lower estimates for the higher and lower characteristic exponents, respectively, of homogeneous n-dimensional linear differential and difference systems with coefficient matrix A(t) satisfying the condition ||A(t)−A(s)|| ≤ δ|t − s|^α, δ > 0, α > 0, t, s ≥ 0. We also prove analogs of these estimates for quasilinear differential and difference systems.