In this paper we consider the following Toda system of equations on a compact surface:{− Δ
u 1= 2 ρ 1 (h 1 eu 1∫ Σ h 1 eu 1 d V g− 1)− ρ 2 (h 2 eu 2∫ Σ h 2 eu 2 d V g− 1)− Δ u 1=− 4 …

Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems Page 1
DOI 10.4171/JEMS/549 J. Eur. Math. Soc. 17, 2037–2068 c European Mathematical Society …

For an asymmetric sinh-Poisson problem arising as a mean field equation of equilibrium
turbulence vortices with variable intensities of interest in hydrodynamic turbulence, we …

We consider the SU (n+ 1) Toda system (S λ){Δ u 1+ 2 λ eu 1− λ eu 2−⋯− λ euk= 0 in Ω, Δ u
2− λ eu 1+ 2 λ eu 2−⋯− λ euk= 0 in Ω,⋮⋱⋮ Δ uk− λ eu 1− λ eu 2−⋯+ 2 λ euk= 0 in Ω, u 1= u …

We are concerned with the following class of equations with exponential nonlinearities: Δ u+
h_1e^ u-h_2e^-2u= 0\qquad in~ B_1 ⊂ R^ 2, Δ u+ h 1 eu-h 2 e-2 u= 0 in B 1⊂ R 2, which is …

We are concerned with a Neumann problem of a one-dimensional sinh-Poisson equation
u′′+ λ sinh u= 0 for 0< x< 1, u′(0)= u′(1)= 0, where λ> 0 is a parameter. A complete …

In this paper, we provide a complete blow-up picture for solution sequences to an elliptic
sinh-Poisson equation with variable intensities arising in the context of the statistical …

The aim of this paper is to use a selection process and a careful study of the interaction of
bubbling solutions to show a classification result for the blow-up values of the elliptic sinh …

We consider the following class of equations with exponential nonlinearities on a compact
surface M: -Δu=ρ_1\left(h_1e^u\smallint_Mh_1e^u-1|M|\right)-ρ_2\left(h_2e …

We study an elliptic problem with exponential nonlinearities describing the statistical
mechanics equilibrium of point vortices with variable intensities. For suitable values of the …