Global stability of solutions of certain third-order nonlinear differential equations. (English) Zbl 1065.34047

Summary: By employing Lyapunov’s second method, we obtain sufficient conditions which ensure that the zero solution of the equation \[ \dddot x+\psi(x,\dot x,\ddot x)\ddot x+f(x,\dot x)=0 \] is globally asymptotically stable. Our result improves and includes some well-known results established in the relevant literature.


34D23 Global stability of solutions to ordinary differential equations