proof of Bendixson’s negative criterion
Suppose that there exists a periodic solution called which has a period of and lies in . Let the interior of be denoted by . Then by Green’s Theorem we can observe that
Since is not identically zero by hypothesis and is of one sign, the double integral on the left must be non zero and of that sign. This leads to a contradiction since the right hand side is equal to zero. Therefore there does not exists a periodic solution in the simply connected region .
|Title||proof of Bendixson’s negative criterion|
|Date of creation||2013-03-22 13:31:07|
|Last modified on||2013-03-22 13:31:07|
|Last modified by||Daume (40)|