On the boundedness of solutions of certain nonlinear vector differential equations of third order. (English) Zbl 1174.34034

Tunç, Cemil

Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 49(97), No. 3, 291-300 (2006).

Summary: This paper is concerned with the boundedness of all solutions of nonlinear vector differential equations of the form \[ \dddot{X}+A(t)F(\ddot{X})+B(t)G(\dot{X})+C(t)H(X)=0. \] Lyapunov’s second method is used as a basic tool in obtaining the criteria for the boundedness of all solutions of the equation.

MSC:

34C11

Growth and boundedness of solutions to ordinary differential equations

Keywords:

boundedness; Lyapunov’s second method; differential equations of third order