Ricerc@Sapienza

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.