Sign-Changing Solutions for the Sinh–Poisson Equation with Robin Boundary Condition

Given ϵ ∈ (0, 1) and λ > 1, we address the existence of solutions for the sinh-Poisson equation with a Robin boundary value condition (Formula presented.) where Ω ⊂ ℝ2 is a bounded smooth domain. We prove two existence results under a suitable relation between ϵ small and λ large. When Ω is symmetric with respect to an axis, we prove the existence of a family of solutions u<inf>ϵ,λ</inf> concentrating at two points with different spin, both located on the symmetry line and close to the boundary. In the second result, we assume Ω is not simply connected and we construct sign-changing solutions concentrating at several points located close to the boundary, each of them on a different connected component of the boundary. © The Hebrew University of Jerusalem 2025.