Uniform stability and boundedness of solutions of nonlinear delay differential equations of the third order

Abstract

In this paper, a complete Lyapunov functional was constructed and used to obtain criteria (when p = 0) for uniform asymptotic stability of the zero solution of the nonlinear delay differential equation (1.1). When p ≠ 0, sufficient conditions are also established for uniform boundedness and uniform ultimate boundedness of solutions of this equation. Our results improve and extend some well known results in the literature.