On the asymptotically cubic generalized quasilinear Schrodinger equations with a Kirchhoff-type perturbation

In this paper, we consider the non-existence and existence of solutions for a generalized quasilinear Schrodinger equation with a Kirchhoff-type perturbation. When the non-linearity h(u) shows critical or supercritical growth at infinity, the non-existence result for a quasilinear Schrodinger equation is proved via the Pohozaev identity. If h(u) shows asymptotically cubic growth at infinity, the existence of positive radial solutions for the quasilinear Schrodinger equation is obtained when b is large or equal to 0 and b is equal to 0 by the variational methods. Moreover, some properties are established as the parameter b tends to be 0.