Fractional Choquard logarithmic equations with Stein-Weiss potential

In the present paper, we are concerned with the following fractional p -Laplacian Choquard logarithmic equation (-Delta)(p)(s)u+V(x)vertical bar u vertical bar(p-2)u+(ln vertical bar center dot vertical bar*vertical bar u vertical bar(p-2)u=(integral(RN) F(y,u)\vertical bar y vertical bar(beta)vertical bar x-y vertical bar(mu) dy) integral(x,u)\vertical bar x vertical bar(beta) in R-N where N = sp >= 2, s is an element of (0, 1), 0 < mu < N, beta >= 0, 2 beta + mu <= N and (-Delta)(s)(p) denotes the fractional p-Laplace operator, the potential V is an element of C(R-N, [0,infinity)), and f : R-N x R -> R is continuous. Under mild conditions and combining variational and topological methods, we obtain the existence of axially symmetric solutions both in the exponential subcritical case and in the exponential critical case. We point out that we take advantage of some refined analysis techniques to get over the difficulty carried by the competition of the Choquard logarithmic term and the Stein-Weiss nonlinearity. Moreover, in the exponential critical case, we extend the nonlinearities to more general cases compared with the existing results. (C) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we study a fractional p-Laplacian Choquard logarithmic equation and obtain the existence of axially symmetric solutions in both the exponential subcritical case and the exponential critical case, using variational and topological methods. We also extend the nonlinearities to more general cases compared with existing results in the exponential critical case.