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

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