Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation
Analysis of PDEs
2020-08-31 v1
Abstract
We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval , under Dirichlet conditions in the exterior of . 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.
Cite
@article{arxiv.2005.09909,
title = {Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation},
author = {Azahara DelaTorre and Gabriele Mancini and Angela Pistoia},
journal= {arXiv preprint arXiv:2005.09909},
year = {2020}
}
Comments
37 pages