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

In the present work, we obtain the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation (-Delta)(p)(s)u+a vertical bar u vertical bar(p-2)u+lambda(ln vertical bar center dot vertical bar*|u|p)|u|(p-2)u=f(u) inR(N), where N = sp, s is an element of (0, 1), p > 2, a > 0, lambda > 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. Published under license by AIP Publishing.