On the Qualitative Behavior of the Solutions for a Kind of Nonlinear Third Order Differential Equations With a Retarted Argument

Abstract

In this paper, by defining a Lyapunov functional, we discuss the stability and the boundedness of the solutions for nonlinear third order delay differential equations of the type: x'''(t) + h(t, x(t), x'(t), x ''(t), x(t - r(t)), x'(t - r(t)), x ''(t - r(t)))x ''(t) + g(x(t - r(t)), x'(t - r(t))) + d(t)psi(x'(t))x'(t) + f(x(t - r(t))) = p(t, x(t), x'(t), x ''(t), x(t - r(t)), x'(t - r(t)), x ''(t - r(t))) Our results include and improve some well-known results in the literature. An example is also given to illustrate the importance of the topic and the results obtained.