Sign-changing solutions for a fractional Choquard equation with power nonlinearity

In this paper, we study the following fractional Choquard equation & nbsp;(-delta)(s)u + V(x)u = (I-alpha * |u|(p))|u|p(-2)u, in R-N, (FC)& nbsp;where s is an element of (0, 1), N >= 3, V(x) is continuous potential function, I-alpha : R-N & nbsp;->& nbsp;R is the Riesz potential of order alpha defined by I alpha(x) = |x|(alpha-N) for every x is an element of R-N \ {0}, alpha is an element of (0, N), * denotes the convolution operator, 2 < p < N+alpha/N-2s = 2(alpha,s)*, 2(alpha,s & nbsp;)* is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and fractional Laplace operator and the operator (-delta)(s) stands for the fractional Laplacian of order s. Combining constraint variational method, quantitative deformation lemma and the Brouwer degree theory, we prove that (FC) possesses one least energy sign-changing solution u0. Moreover, we show that 2(p-2/p-1) times and strictly less than four times the ground state energy. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.