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Zbl 1166.34311
Ademola, A.T.; Kehinde, R.; Ogunlaran, O.M.
A boundedness theorem for a certain third order nonlinear differential equation. (English)
[J] J. Math. Stat. 4, No. 2, 88-93 (2008). ISSN 1549-3644

The authors consider the following nonlinear third order differential equation $$ {x}''' + f(x,{x}',{x}''){x}'' + g(x,{x}') + h(x,{x}',{x}'') = P(t,x,{x}',{x}''),$$ where $f$, $g$, $h$ and $P$ are assumed to be continuous in all arguments, further, the existence of continuous partial derivatives of these functions with respect to some arguments are assumed. The authors prove a theorem, which guarantees the ultimate boundedness of all solutions of the preceding equation. To prove the theorem, a complete Yoshizawa function is used a basic tool.
[Cemil Tunç (Van)]

MSC 2000:: *34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: boundedness; third order; nonlinear differential equation

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