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 ${(-\mathrm{\Delta })}_p^{s}u+a|u{|}^{p-2}u+\lambda (\ln |\cdot |*|u{|}^p)|u{|}^{p-2}u=f(u)\mathrm{i}\mathrm{n}{\mathbb{R}}^N$ , where N = sp, s ∈ (0, 1), p > 2, a > 0, λ > 0, and $f:\mathbb{R}\to \mathbb{R}$ is 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. Moreover, when f has subcritical growth, we prove the existence of infinitely many solutions via genus theory.