Boundedness results for a certain third order nonlinear differential equation. (English) Zbl 1201.34055

Ademola, Timothy A.; Ogundiran, Michael O.; Arawomo, Peter O.; Adesina, Olufemi Adeyinka

Appl. Math. Comput. 216, No. 10, 3044-3049 (2010).

The authors consider a class of third order non-linear differential equations of the form
\[ \dddot{x} + f(\ddot {x}) + g(\dot {x}) + h(x) = p(t,x,\dot {x},\ddot {x}), \tag{1} \]
where \(f, g, h \in C(\mathbb R ,\mathbb R )\), \(p \in C(\mathbb R ^ + \times \mathbb R ^3,\mathbb R )\), \( \mathbb R ^ + = [0,\infty )\). The authors give some new sufficient conditions which guarantee the boundedness and uniform ultimate boundedness of the solutions (1). By defining an appropriate Lyapunov function, they prove their main results.

Reviewer: Cemil Tunç (Van)

MSC:

34C11

Growth and boundedness of solutions to ordinary differential equations

Keywords:

third order nonlinear differential equation

References:

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