Structure and stability of certain class of differential equations (Q1076888)

Using Lyapunov's second method the author gives sufficient conditions for the stability and global asymptotic stability of the zero solution of the equation \(x^{(n)}+b_ 1x^{(n-1)}+b_ 2x^{(n-2)}+...+b_ nx=0,\) where \(b_ i=f(t,x,x^{(1)},x^{(2)},...,x^{(n-1)})a_ i\) if i is odd, \(b_ i=a_ i\) if i is even, \(a_ i=const\).