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New results on the asymptotic behavior of a third-order nonlinear differential equation. (English) Zbl 1198.34085
The author studies the equation $x'''+g(x,x')x''+f(x,x') = p(t) ,$ where $$g,f,g_{x},f_{x}\in C({\mathbb R}\times {\mathbb R},{\mathbb R})$$ and $$p\in C([0,\infty ),{\mathbb R})$$. It is assumed that the solutions $$x(t)$$ of the considered equation exist and are unique. Sufficient conditions are established such that for all solutions there holds: (a) There exists a constant $$D>0$$ such that $$|x^{(i)}(t)|\leq D$$, for sufficiently large $$t$$. (b) $$x^{(i)}(t)\rightarrow 0$$, as $$t\rightarrow \infty$$; $$i=0,1,2$$.

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations
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