Normalized ground states for fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities

Abstract

In this paper, we study the existence of normalized ground states for nonlinear fractional Kirchhoff equations with Sobolev critical exponent and mixed nonlinearities in R3. To overcome the special difficulties created by the nonlocal term and fractional Sobolev critical term, we develop a perturbed Pohožaev method based on the Brézis–Lieb lemma and monotonicity trick. Using the Pohožaev manifold decomposition and fibering map, we prove the existence of a positive normalized ground state. Moreover, the asymptotic behavior of the obtained normalized solutions is also explored. These conclusions extend some known ones in previous papers.