For singular mean field equations defined on a compact Riemann surface, we prove the
uniqueness of bubbling solutions as far as blowup points are either regular points or non …

For domains of first kind we describe the qualitative behavior of the global bifurcation
diagram of the unbounded branch of solutions of the Gelfand problem crossing the origin. At …

We are concerned with the Moser-Trudinger problem\begin {equation*}\begin {cases}-\Delta
u=\lambda ue^{u^ 2}~~ &\mbox {in}~\Omega,\\[0.5 mm] u> 0~~ & {\text {in}~\Omega},\\[0.5 …

For singular mean field equations defined on a compact Riemann surface, we prove the
uniqueness of bubbling solutions if some blowup points coincide with the singularities of the …

In this paper, we study several relations of Morse indices of the blow-up solutions to the
exponentially dominated elliptic boundary problem in two dimensions. We also study the …

We consider the Gelfand problem {-Δ u= ρ^ 2V (x) e^ u&\quad in Ω\u= 0&\quad on ∂ Ω.,-Δ
u= ρ 2 V (x) eu in Ω u= 0 on∂ Ω, where Ω Ω is a planar domain and ρ ρ is a positive small …

The aim of this note is to present the first qualitative global bifurcation diagram of the
equation $-\Delta u=\mu| x|^{2\alpha} e^ u $. To this end, we introduce the notion of domains …

The aim of this note is to present the first qualitative global bifurcation diagram of the
equation $-\Delta u=\mu| x|^{2\alpha} e^{u} $. To this end, we introduce the notion of …

We are concerned with the blow-up analysis of mean field equations. It has been proven in
[6] that solutions blowing-up at the same non-degenerate blow-up set are unique. On the …

We are concerned with the mean field equation with singular data on bounded domains. By
assuming a singular point to be a critical point of the 1-vortex Kirchhoff-Routh function, we …