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

The authors consider a class of third order non-linear differential equations of the form

$\stackrel{⃛}{x}+f\left(\stackrel{¨}{x}\right)+g\left(\stackrel{˙}{x}\right)+h\left(x\right)=p\left(t,x,\stackrel{˙}{x},\stackrel{¨}{x}\right),\phantom{\rule{2.em}{0ex}}\left(1\right)$

where $f,g,h\in C\left(ℝ,ℝ\right)$, $p\in C\left({ℝ}^{+}×{ℝ}^{3},ℝ\right)$, ${ℝ}^{+}=\left[0,\infty \right)$. 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.

##### MSC:
 34C11 Qualitative theory of solutions of ODE: growth, boundedness
##### Keywords:
third order nonlinear differential equation
##### References:
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