On the mass concentration of normalized ground state solutions for non-autonomous Kirchhoff equations

Abstract

In this paper, we focus on a class of non-autonomous Kirchhoff equations, that is, $-(a+b{\int }_{R^3}{|\nabla u|}^2\text{d}x)\Delta u-\lambda u=K\left(x\right){\left|u\right|}^{p-2}u$ in $R^3$, where $a,b>0$ are constants, $\lambda \in R$ is unknown and appears as a Lagrange multiplier, $2<p<6$ and $K:R^3\to R$ is a potential function. Under certain assumptions on the potential $K$, the concentration behavior of normalized ground state solutions is analyzed by using variational methods.