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arXiv · 2005.09909

Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation

Azahara DelaTorre·Gabriele Mancini·Angela Pistoia
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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 $I$, 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.

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Azahara DelaTorre, Gabriele Mancini, Angela Pistoia. 2020-05-20. Sign-changing solutions for the one-dimensional non-local sinh-Poisson equation. https://doi.org/10.1515/ans-2020-2103

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