Multiple solutions to a class of generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

In this paper, we consider a class of generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation. Under the assumption that the potential may be vanishing at infinity, the existence of both the ground state and the ground state sign-changing solutions is established. Furthermore, the behavior of these solutions is studied when the perturbation vanishes. It is a surprise that we find an interesting phenomenon about the monotonicity for the quotient function as a byproduct.