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arXiv · 2502.04532

Multiple nodal solutions of planar Stein-Weiss equations

Eudes M. Barboza·Eduardo De S. Böer·Olímpio H. Miyagaki·Claudia R. Santana
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Abstract

In this paper, our goal is to investigate the existence of multiple nodal solutions to a class of planar Stein-Weiss problems involving a nonlinearity $f$ with subcritical or critical growth in the sense of Trudinger-Moser. To achieve this, we combine a gluing approach with the Nehari manifold argument. We demonstrate that for any positive integer $k\in \mathbb{N}$, the problem studied has at least one radially symmetrical ground state solution that changes sign exactly $k$-times.

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Eudes M. Barboza, Eduardo De S. Böer, Olímpio H. Miyagaki, Claudia R. Santana. 2025-02-06. Multiple nodal solutions of planar Stein-Weiss equations. https://arxiv.org/abs/2502.04532

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