International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 99-110
doi:10.1155/S0161171291000108
On point-dissipative systems of differential equations with quadratic nonlinearity
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.
Abstract
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).