On the Stability of Solutions of Nonlinear Differential Equations of Fifth Order With Delay

Abstract

Criteria for global asymptotic stability of a null solution of a nonlinear differential equation of fifth order with delay x((5))(t) + psi(x (t - r); x'(t - r); x''' (t - r); x'''(t - r); x((4)) (t - r))x((4)) (t) + f (x ''(t - r); x'''(t- r)) + alpha(3)x ''(t) + alpha(4)x'(t) + alpha(5)x(t) = 0 are obtained by using Lyapunov's second method. By defining a Lyapunov functional, sufficient conditions are established, which guarantee the null solution of this equation is globally asymptotically stable. Our result consists of a new theorem on the subject.