A New Result on the Stability of Solutions of a Nonlinear Differential Equation of Third-Order With Finite Lag

Abstract

Criteria for uniform stability of the trivial solution of the nonlinear third order delay differential equation x '''(t) + a(1)(t) x ''(t) + a(2)(t)psi(x(t - r(t)), x '(t - r(t))) + a(3)x(t) = 0 are obtained by Lyapunov's second method. By constructing a Lyapunov functional, sufficient conditions are established which guarantee the trivial solution of this equation is uniformly stable. Our result improves a known result in the literature.