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 (−Δ)psu+a|u|p−2u+λ(ln|⋅|*|u|p)|u|p−2u=f(u)inRN, where N = sp, s ∈ (0, 1), p > 2, a > 0, λ > 0, and f:R→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.