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.


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