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.


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