A NEW BOUNDEDNESS RESULT TO NONLINEAR DIFFERENTIAL EQUATIONS OF THIRD ORDER WITH FINITE LAG

摘要

Criteria for boundedness of solutions to the nonlinear third order delay differential equationrnx'"(t) + φ(x(t),x'(t), x"(t))x"(t) + ψ(x(t - r(t)),x'(t - r(t))) + h(x(t - r(t))) = p(t,x(t),x(t - r(t)),x'(t),x'(t - r(t)),x"(t))rnare obtained by Lyapunov's second method. By introducing a Lyapunov functional, sufficient conditions are established that guarantee that all solutions of this equation are bounded. An example is also given to illustrate the importance of result obtained. Our findings improve a result existing in the literature to boundedness of solutions for this delay differential equation.