On the qualitative behaviors of solutions to a kind of nonlinear third order differential equations with retarded argument - Tunç, Cemil (Italian Journal of Pure and Applied Mathematics, 2011)
In this paper, with use of a Lyapunov functional, we discuss stability and boundedness of solutions to a kind of nonlinear third order differential equation with retarded argument: x'''(t) + h(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' r(t))) + f(x(t - r(t))) = p(t, x(t), x'(t), x(t - r(t)), x'(t - r(t)), x''t)), when p(t, x(t), x0(t), x(t ¡ r(t)), x0(t ¡ r(t)), x00(t)) = 0 and ≠ 0, respectively. Our results include and improve some well-known results in the literature. An example is also given to illustrate the importance of results obtained and the topic.