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% begin{eqnarray*} &&x^{(5)}(t)+psi (x(t-r),x^{prime }(t-r),x^{prime prime }(t-r),x^{prime prime prime }(t-r),x^{(4)}(t-r))x^{(4)}(t) \ &&quad+f(x^{prime prime }(t-r),x^{prime prime prime }(t-r))+alpha _{3}x^{prime prime }(t)+alpha _{4}x^{prime }(t)+alpha _{5}x(t)=0 end{eqnarray*} are obtained by using Lyapunov\u27s 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