On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation - Li, Guofa; Qiu, Chong; Cheng, Bitao; Wang, Wenbo (Frontiers in Physics, 2023)
In this paper, we consider the nonexistence and existence of solutions for a generalized quasilinear Schrödinger equation with a Kirchhoff-type perturbation. When the nonlinearity $h(u)$ is critical or supercritical growth at infnity, the nonexistence result for quasilinear Schrödinger equation is proved via Pohožaev identity. If $h(u)$ is asymptotically cubic growth at infinity, the existence of positive radial solutions for quasilinear Schrödinger equation are obtained for $b$ 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 $0$.