Non-simple blow-up solutions for the Neumann two-dimensional sinh-Gordon equation

For the Neumann sinh-Gordon equation on the unit ball B ⊂R^2 $-\Delta u = λ^+(e^u/\int_B e^u-1/\pi)-λ^-(e^{-u}/\int_B e^{-u}-1/\pi)$ in $B$, $∂_ν=0$ on $\partial B$ we construct sequence of solutions which exhibit a multiple blow up at the origin, where λ± are positive parameters. It answers partially an open problem formulated in Jost et al. [Calc Var Partial Diff Equ 31(2):263–276]