Existence and Asymptotics of Normalized Ground States for a Sobolev Critical Kirchhoff Equation

In the present paper, we investigate the existence and asymptotic properties of normalized solutions for the following Kirchhoff-type equation with Sobolev critical growth { I-(a + b integral(3)(R) |del u|(2)dx)triangle u + lambda u = mu|u|(p-2)u + |u|(4)u, in R-3, (P) u > 0, integral(3)(R) |u|(2)dx = m(2), in R-3, where a, b, m, mu > 0 and14/3 < p < 6. With the aid of the Sobolev subcritical approximation method that is the first time used to consider mass constrained Kirchhoff-type problems, and Schwartz symmetrization rearrangements, we obtain the existence of normalized ground states. Moreover, the asymptotic behavior of these solutions is also studied.