Existence and limit behavior of normalized ground state solutions for a class of non-autonomous Kirchhoff equations

In this paper, we consider a class of non-autonomous Kirchhoff equations with two nonnegative potentials in \({\mathbb {R}}^N\) ${\mathbb{R}}^N$  ( \(N =1,2,3\) $N=1,2,3$ ). Under certain basic assumptions on the potentials, the existence and nonexistence of normalized ground state solutions are classified completely by investigating equivalently the associated \(L^2\) $L^2$ -constrained minimization problem. Based on some delicate estimates of the corresponding energy functional, the limit behavior of normalized ground state solutions is also analyzed as the prescribed \(L^2\) $L^2$ -norm goes to infinity. Our main results extend and complement some known related results in the literature.