Existence and multiplicity of solutions for the fractional $p$-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth

Abstract

In the present work we obtain the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation $(-\Delta {)}_p^{s}u+|u{|}^{p-2}u+(\ln |\cdot |\ast |u{|}^p)|u{|}^{p-2}u=f(u)\text{ in }{\mathbb{R}}^N$ , where $N=sp$, $s\in (0,1)$, $p>2$, $a>0$, $\lambda >0$ and $f:\mathbb{R}\to \mathbb{R}$ a continuous nonlinearity with exponential critical and subcritical growth. We guarantee the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution under critical and subcritical growth. Morever, when $f$ has subcritical growth we prove the existence of infinitely many solutions, via genus theory.

arXiv comment28 pages. arXiv admin note: text overlap with arXiv:2011.12806

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• Stationary waves with prescribed $L^2$-norm for the planar Schrödinger-Poisson system
• The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate
• Bound states of two-dimensional Schrödinger-Newton equations
• The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth

Cited by in corpus (2)

• Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
• On the existence and multiplicity of solutions for the $N$-Choquard logarithmic equation with exponential critical growth