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

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 Hindawi Publishing Corporation. 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 ′ = A x + f ( x ) of nonlinear vector differential equations, where the nonlinear term f ( x ) is quadratic with orthogonality property x T f ( x ) = 0 for all x , is point-dissipative if u T A u < 0 for all nontrivial zeros u of f ( x ) .