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

Abstract

In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-\Delta {)}^{\frac{1}{2}}u+au+\lambda (\ln |\cdot |\ast |u{|}^2)u=f(u)\text{ in }\mathbb{R}$, 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.

26 pages. arXiv admin note: text overlap with arXiv:2011.01260