Global attractors of non-autonomous quasi-homogeneous dynamical systems (Q2778474)

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.