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Original Articles

On p-homogeneous systems of differential equations and their linear perturbations

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Pages 225-247 | Received 16 Jul 2004, Accepted 24 Aug 2004, Published online: 25 Jan 2007
 

Abstract

Long-time asymptotic properties of the solutions of the system

where f (u) is positive homogeneous of degree p>1, are studied. We also consider the corresponding linearly perturbed system
It is shown that if AI, then the global existence of all solutions for one value of α implies that the same property holds for all α, and that all solutions converge to the origin when α<0. On the other hand, it is shown that the addition of a matrix for which A u is inward in the sense that u · A u <0 for u ≠ 0 can turn a p-homogeneous system all of whose solutions are bounded into one which has solutions which blow up in a finite time.

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