Bendixson-Dulac criterion

Consider the dynamical system $˙ 𝐱 = 𝑓 (𝐱)$ Let $𝑅 \subseteq ℝ 2$ be a simply-connected set, and $𝜑 \in 𝖬 𝖺 𝗇 1 (𝑅, ℝ)$ . If

d i v (𝐵 𝑓)

has the same sign Almost everywhere then the system has no nonconstant periodic solutions.

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