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
Anil K. Bose
, Alan S. Cover
and James A. Reneke
Department of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USA
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).