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.

Automated summary

In this work, we investigate the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation under different growth conditions, ensuring the existence of nontrivial solutions and ground state solutions. The study also proves the existence of infinitely many solutions under subcritical growth of the nonlinearity function.