A degree-counting formula for a Keller-Segel equation on a surface with boundary

Mohameden Ahmedou, Zhengni Hu, Heming Wang

In this paper, we consider the following Keller-Segel equation on a compact Riemann surface $(\Sigma ,g)$ with smooth boundary $\partial \Sigma$: \[ -Δ_g u = ρ\Big(\frac{V e^u}{\int_Σ V e^u \…