Resumen de On the Sharp Existence of Normalized Ground State Solutions for Non-Autonomous Kirchhoff Equations

Miao Du, Xiaohan Gao

• In this paper, we deal with a class of non-autonomous Kirchhoff equations, namely, −(a + b RN |∇u| 2 dx)u − μu = K(x)|u|p−2u in RN , where 1 ≤ N ≤ 4, a, b > 0 are constants,μ ∈ R is unknown and appears as a Lagrange multiplier, 2 < p < 2∗ and K ∈ C(RN , R) is a bounded potential function satisfying infRN K > 0. Under certain additional assumptions on the potential K, the sharp existence of normalized ground state solutions is obtained by investigating equivalently the associated L2-constrained minimization problem. Our main results extend and improve the corresponding results in the previous papers.