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Global attractors of non-autonomous quasi-homogeneous dynamical systems. (English) Zbl 1008.34046
The author shows that a nonautonomous quasi-homogeneous differential equation $$x'=f(x)+F(x,t)$$, where $$f(\lambda x)=\lambda ^mf(x)$$ for $$\lambda >0$$ and $$|F(x,t)||x|^{-m}\to 0$$ as $$|x|\to \infty$$, admits a compact global attractor if the homogeneous differential equation $$x'=f(x)$$ is asymptotically stable. The general result is applied to differential equations both in finite-dimensional spaces and in infinite-dimensional spaces, such as ordinary differential equations in Banach space and some types of evolutional partial differential equations.

##### MSC:
 34D45 Attractors of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces
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