Note on normalized solutions to a kind of fractional Schro<spacing diaeresis>dinger equation with a critical nonlinearity

In this paper, we study normalized solutions of the fractional Schro<spacing diaeresis>dinger equation with a critical nonlinearity { (-Delta)(s)u = lambda u + |u|p(-2) u + |u|(2 & lowast;s-2) u,x is an element of R-N , integral R-N u(2) dx = a(2), u is an element of H-s (R-N), where N >= 2, s is an element of (0,1), a > 0, 2 < p < 2(s)(& lowast;)- (2N)|(N-2s) and (-Delta)(s) is the fractional Laplace operator. In the purely L-2-subcritical perturbation case 2 < p < 2 + (4s)|(N) , we prove the existence of a second normalized solution under some conditions on a , p , s , and N . This is a continuation of our previous work ( Z. Angew. Math. Phys. , 73 (2022) 149) where only one solution is obtained.