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arXiv · 2011.12806

The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth

Eduardo de Souza Böer·Olímpio H. Miyagaki
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Abstract

In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-\Delta)^{\frac{1}{2}} u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ in } \mathbb{R}$, for $ a>0 $, $ \lambda >0 $ and a nonlinearity $f$ with exponential critical growth. We prove the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution under exponential critical and subcritical growth. Morever, when $ f $ has subcritical growth we guarantee the existence of infinitely many solutions, via genus theory.

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Eduardo de Souza Böer, Olímpio H. Miyagaki. 2020-11-25. The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth. https://arxiv.org/abs/2011.12806

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