Boundedness of solutions of a third-order nonlinear differential equation. (English) Zbl 1082.34514

Tunç, Cemil

JIPAM, J. Inequal. Pure Appl. Math. 6, No. 1, Paper No. 3, 6 p. (2005).

Summary: Sufficient conditions are established for the boundedness of all solutions of \[ \dddot x+f(x,\dot x,\ddot x)\ddot x+g(x,\dot x)+h(x,\dot x,\ddot x)=p(t,x,\dot x,\ddot x). \] We also present some sufficient conditions, which ensure that the limits of first- and second-order derivatives of the solutions of the equation tend to zero as \(t\to\infty\).

MSC:

34C11

Growth and boundedness of solutions to ordinary differential equations