×

zbMATH — the first resource for mathematics

Asymptotic behavior of a third-order nonlinear differential equation. (English) Zbl 1054.34078
Summary: Consider the third-order nonlinear differential equation \[ x'''+ \psi(x, x')x''+ f(x, x')= p(t), \] where \(\psi\), \(f\), \(f_x\in C(\mathbb{R}\times \mathbb{R},\mathbb{R})\) and \(p\in C([0, \infty),\mathbb{R})\). We obtain sufficient conditions for every solution to the equation to be bounded; we also establish criteria for every solution to the equation to converge to zero.

MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Barbashin, E.A., Lyapunov functions, (1970), Nauka Moscow · Zbl 0241.34057
[2] Ezeilo, J.O.C., Stability results for the solutions of some third and fourth order differential equations, Ann. mat. pura appl., 66, 233-249, (1964) · Zbl 0126.30403
[3] Gera, M.; Graef, J.R.; Gregus, M., On oscillatory and asymptotic properties of solutions of certain nonlinear third order differential equations, Nonlinear anal., 32, 417-425, (1998) · Zbl 0945.34021
[4] Qian, C., On global stability of third-order nonlinear differential equations, Nonlinear anal., 42, 651-661, (2000) · Zbl 0969.34048
[5] Reissig, R.; Sansone, G.; Conti, R., Nonlinear differential equations of higher order, (1974), Noordhoff Leyden · Zbl 0275.34001
[6] Tunc, C., On the ultimate boundedness result of the solutions of certain fourth order differential equation, Ann. differential equations, 14, 475-485, (1998) · Zbl 0967.34055
[7] Yoshizawa, T., Asymptotic behavior of solutions of a system of differential equations, Contrib. differential equations, I, 371-387, (1963) · Zbl 0127.30802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.