Liapunov exponents for higher-order linear differential equations whose characteristic equations have variable real roots

We consider the linear differential equation $$ sum_{k=0}^n a_k(t)x^{(n-k)}(t)=0quad tgeq 0, ; ngeq 2, $$ where $a_0(t)equiv 1$, $a_k(t)$ are continuous bounded functions. Assuming that all the roots of the polynomial $z^n+a_1(t)z^{n-1}+ dots +a_n(t)$ are real and satisfy the inequality $r_k(t) Keywords Linear differential equations --- Liapunov exponents --- exponential stability