Dulacβs criteria
Let
Λπ±=π(π±)
be a planar system where π=(π,π)t and π±=(x,y)t. Furthermore πβC1(E) where E is a simply connected region of the plane. If there exists a function p(x,y)βC1(E) such that β(p(x,y)π)βx+β(p(x,y)π)βy (the divergence of the vector field p(x,y)π, ββ p(x,y)π) is always of the same sign but not identically zero then there are no periodic solution in the region E of the planar system. In addition, if A is an annular region contained in E on which the above condition is satisfied then there exists at most one periodic solution in A.
Title | Dulacβs criteria |
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Canonical name | DulacsCriteria |
Date of creation | 2013-03-22 13:37:09 |
Last modified on | 2013-03-22 13:37:09 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 5 |
Author | Daume (40) |
Entry type | Theorem |
Classification | msc 34C25 |