Nodal solution for a planar problem with fast increasing weights

Giovany M. Figueiredo, Marcelo F. Furtado, Ricardo Ruviaro

DOI: http://dx.doi.org/10.12775/TMNA.2019.070

Abstract


In this paper we prove the existence of a sign-changing solutions for the equation $$ -\Delta u - \frac{1}{2} ( x \cdot \nabla u) = f(u), \quad x \in \mathbb{R}^2, $$ where $f$ has exponential critical growth in the sense of the Trudinger-Moser inequality. In the proof we apply variational methods.

Keywords


Nodal solutions; critical exponential growth; self-similar solutions

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