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, $$0\leq r(t)\leq \gamma$$, $$\gamma$$ 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.

MSC:

 34K20 Stability theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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References:

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