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

arXiv2011.12806MaRDI QIDQ6354569

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Publication date: 25 November 2020

Abstract: In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-Delta{)}^{frac12}u+au+lambda(ln|cdot|ast|u{|}^2)u=f(u)extrminmathbbR$, 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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