International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 99-110

On point-dissipative systems of differential equations with quadratic nonlinearity

Anile K. Bose, Alan S. Cover, and James A. Reneke

Department of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USA

Received 25 April 1990

Copyright © 1991 Anile K. Bose et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The system x=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if uTAu<0 for all nontrivial zeros u of f(x).