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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
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References:
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