I am looking for a place to read the proofs of Bendixsons and Dulac-Bendixsons theorems. Namely let D be a simply connected set and the following system be defined in D. $$\dot x=P(x,y)$$ $$\dot y=Q(x,y)$$
Then the following theorems hold.
Theorem: (Bendixon) Given that $P_x+Q_y$ doesn't change sing in D, the system does not have a periodical solution.
Theorem: (Dulac-Bendixon) If a function $B(x,y)\in C^1(D)$ exists, such that $(BP)_x+(BQ)_y$ doesn't change sing in D. Then the system does not have a periodical solution.