On the instability of solutions of certain non-autonomous vector differential equations of fifth order

Abstract

By using Lyapunov’s function approach [13], some new results were established, which guarantee that the zero solution of non-linear vector differential equations of the form

$$X^{(5)}+a(t)\text{Ψ}(\dot{X},\ddot{X})\stackrel{⃛}{X}+b(t)\text{Φ}(X,\dot{X},\ddot{X},\stackrel{⃛}{X},X^{(4)})+c(t)\text{Θ}(\dot{X})+F(X)=0$$

is unstable.