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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