The existence of ground state normalized solution for Kirchhoff equation

Abstract

In this paper, we study the existence of ground state solution for the following Kirchhoff equation with combined nonlinearities − ( a + b ∫ R N | ∇ u | 2 ) Δ u = λ u + | u | p − 2 u + μ | u | q − 2 u in R N , 1 ≤ N ≤ 3 with prescribed mass , where , , . Under certain assumptions on the parameter μ, we obtain the existence of normalized solution , where .