Fractional Choquard logarithmic equations with Stein-Weiss potential

Abstract

In the present paper, we are concerned with the following fractional p-Laplacian Choquard logarithmic equation(−Δ)psu+V(x)|u|p−2u+(ln⁡|⋅|⁎|u|p)|u|p−2u=(∫RNF(y,u)|y|β|x−y|μdy)f(x,u)|x|βinRN, where N=sp≥2, s∈(0,1), 0<μ<N, β≥0, 2β+μ≤N and (−Δ)ps denotes the fractional p-Laplace operator, the potential V∈C(RN,[0,∞)), and f:RN×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.