The energy level transition for nonlinear Kirchhoff equation under a perturbation of potential

Abstract

In this paper, we study the energy level transition behavior for the nonlinear Kirchhoff equation with a potential and a pure power nonlinearity. The potential function is assumed to be a perturbation of a positive constant. Under a negative perturbation, the persistence for ground state solution is demonstrated. It is also proved that a positive perturbation excludes the ground state solution while ensuring the existence of the bound state solution with high energy. Our approach is based on the variational method, aided by global compactness and linking theorem.