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Stability and boundedness of a kind of third-order delay differential system. (English) Zbl 1056.34078
The author considers the third-order nonlinear differential equation $$ x^{(3)} + a \ddot x + g( \dot x(t-r(t))) + f(x(t-r(t)))=p(t), $$ where $a$ is a positive constant, $0\le r(t)\le \gamma$, $\gamma$ is some positive constant, $g(x), f(x), p(t)$ are continuous, and $g(0)=f(0)=0$. The aim of the paper is to derive conditions for the stability and boundedness of the solutions to this problem in the cases $p\equiv 0$ and $p\not \equiv 0$, respectively.

34K20Stability theory of functional-differential equations
34K12Growth, boundedness, comparison of solutions of functional-differential equations
Full Text: DOI
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