Zhong-Wei Tang

Topological degree for singular $N$-mean field equations

We determine the Leray--Schauder degree of the singular Dirichlet $N$-mean field equation on a smooth bounded domain in $\mathbb{R}^N$, $N\geq2$, for every positive nonresonant parameter and singular exponents $-1<\alpha_i\leq0$. The formula depends only on the Euler characteristic of the domain and the weights $(1+\al...