A new boundedness result to nonlinear differential equations of third order with finite lag. (English) Zbl 1178.34080
Summary: Criteria for boundedness of solutions to the nonlinear third order delay differential equation $$\multline x'''(t) + y(x(t),x''(t), x''(t))x''(t) +\psi(x(t - r(t)),\ x'(t - r(t))) + h(x(t - r(t))) =\\ = p(t, x(t),x(t- r(t)),x'(t),x'(t - r(t)), x''(t))\endmultline$$ are 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.
|34K12||Growth, boundedness, comparison of solutions of functional-differential equations|