Normalized solutions for the fractional Choquard equations with Sobolev critical and double mass supercritical growth

In the present paper, we study the following Sobolev critical fractional Choquard equation {(-Delta)(s)u + lambda u = eta[vertical bar x vertical bar(-mu)*vertical bar u vertical bar(p)]vertical bar u vertical bar(p-2) u + vertical bar u vertical bar(2*s-2)u, in R-N, integral(RN)vertical bar u vertical bar(2)dx = m(2), where m, eta > 0, 0 < s < 1, N >= 2, 0 < mu < 2s, 2 + 2 s-mu/N < p <= 2N-mu+s.2(s)*/N < 2 mu(*)(,s) := 2N-mu/N-2s, 2(s)(*) := 2N/N-2s is the fractional Sobolev critical exponent. By virtue of a fiber map and the concentration-compactness principle, we obtain a couple of normalized solutions to the above equation for large eta, which extends and improves the results in Li et al. and Yang, and almost no one has studied the double mass supercritical cases.