  We study the existence of sign-changing solutions for a non-local version of
the sinh-Poisson equation on a bounded one-dimensional interval $I$, under
Dirichlet conditions in the exterior of $I$. This model is strictly related to
the mathematical description of galvanic corrosion phenomena for simple
electrochemical systems. By means of the finite-dimensional Lyapunov-Schmidt
reduction method, we construct bubbling families of solutions developing an
arbitrarily prescribed number sign-alternating peaks. With a careful analysis
of the limit profile of the solutions, we also show that the number of nodal
regions coincides with the number of blow-up points.
