Dulac’s criteria



be a planar system where 𝐟=(𝐗,𝐘)t and 𝐱=(x,y)t. Furthermore 𝐟∈C1⁒(E) where E is a simply connected region of the plane. If there exists a function p⁒(x,y)∈C1⁒(E) such that βˆ‚β‘(p⁒(x,y)⁒𝐗)βˆ‚β‘x+βˆ‚β‘(p⁒(x,y)⁒𝐘)βˆ‚β‘y (the divergence of the vector field p⁒(x,y)⁒𝐟, βˆ‡β‹…p⁒(x,y)⁒𝐟) 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 Dulac’s criteria
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