Properties of the Constrained Minimizers for Kirchhoff Type Energy Functionals With Inhomogeneous Interactions

ABSTRACT We consider the properties of the constrained minimizers for a class of Kirchhoff type energy functionals with inhomogeneous interactions . When , it is known that there exists , where is the unique positive radial solution of , such that the minimizer exists if and only of . The aim of this paper is to investigate the limiting behavior of minimizers as approaches 0 for any . More specially, we prove that all the mass of the minimizers must concentrate at a global minimum point of trapping potential as approaches 0, where is also a global maximum point of .