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Boundedness and convergence of solutions of a second-order nonlinear differential system. (English) Zbl 0983.34021
The author considers the second-order nonlinear differential system $\dot{x}= \frac{1}{a(x)}[h(y)-F(x)],\qquad \dot{y}= -a(x)[g(x)-e(t)].$ Sufficient and necessary conditions for all solutions to be bounded and to converge to zero are presented. The obtained results are applied to the differential equation $\ddot{x}+f_1(x)\dot{x}+f_2(x)\dot{x}^2+g(x)=e(t).$

##### MSC:
 34C11 Growth and boundedness of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
##### Keywords:
system of differential equations
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##### References:
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