A New Result on the Stability of Solutions of a Nonlin-ear Differential Equation of Third-order with Finite Lag

摘要

Criteria for uniform stability of the trivial solution of the nonlinear thirdorder delay differential equation x" (t) + a1(t)x"(t) + az(x (t — r (t)), (t — r(t))) + a3x(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 equationis uniformly stable. Our result improves a known result in the literature.