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arXiv · 2107.13281

Existence of normalized solutions for the planar Schr\"odinger-Poisson system with exponential critical nonlinearity

Claudianor O. Alves·Eduardo de S. Boër·Olímpio H. Miyagaki
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Abstract

In the present work we are concerned with the existence of normalized solutions to the following Schr\"odinger-Poisson System $$ \left\{ \begin{array}{ll} -\Delta u + \lambda u + \mu (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ \ in \ } \mathbb{R}^2 , \\ \intR |u(x)|^2 dx = c,\ c> 0 , \end{array} \right. $$ for $\mu \in \R $ and a nonlinearity $f$ with exponential critical growth. Here $ \lambda\in \R$ stands as a Lagrange multiplier and it is part of the unknown. Our main results extend and/or complement some results found in \cite{Ji} and \cite{[cjj]}.

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Claudianor O. Alves, Eduardo de S. Boër, Olímpio H. Miyagaki. 2021-07-28. Existence of normalized solutions for the planar Schr\"odinger-Poisson system with exponential critical nonlinearity. https://arxiv.org/abs/2107.13281

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