Symmetry of positive solutions for Choquard equations with fractionalp-Laplacian

Symmetry of singular solutions for a weighted Choquard equation involving the fractional <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian

“…Using this approach, Ma-Zhang [18] proved the symmetry and nonexistence of positive solutions of (2) in the case 0 < β < 2 and p = 2. Very recently, Ma-Zhang [20] partially extended this result to the case p > 2. They proved that if u ∈…”

“…After the direct method of moving planes was introduced, a series of fruitful results have been obtained. Many of them improve previous ones established by using other methods, we refer to [9,11,12,14,16,18,20,24] and references therein.…”

“…Moreover, in our result, u is allowed to blow up at zero. In stead of using the equivalent fractional system as in [18,20], we exploit a direct method of moving planes for the weighted Choquard nonlinearity. This approach allows us to cover the full range 0 < β < n and α > 0 in our results.…”

Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian

“…In relation to the study of many problems in physics, Choquard equation received considerable attention [4,9,11]. Moroz and Schaftingen [9] established regularity and positivity of the groundstates for the following nonlinear Choquard or Choquard-Pekar equation…”

“…Ma and Zhang [11] studied the radial symmetry of positive solutions for Choquard equation with fractional p-Laplacian:…”