Sign-changing solutions for a class of fractional Choquard equation with the Sobolev critical exponent in R 3

In this paper, we study the following fractional Choquard equation with critical exponent (A)+(JP)uP2u+uu in R. where (1,1), a <euro> (20,3) and <p<22 is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality, 2 is the fractional Sobolev critical exponent and the operator (-A)" stands for the fractional Laplacian of order o. Based on the above assumptions, we establish the existence of positive ground state solutions, and if pe(), we also have the corresponding regular property. Subsequently, by introducing some other additional hypotheses on a, a, pand with the help of quantitative deformation lemma, we employ constrained minimization arguments on the sign-changing Nehari manifold to obtain the existence of ground state sign-changing solutions. 1 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, Al training, and similar tecnologies.