The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth
| Autor: | Böer, Eduardo de Souza, Miyagaki, Olímpio H. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 26 pages. arXiv admin note: text overlap with arXiv:2011.01260 |
| Databáze: | arXiv |
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