AUTHOR=Li Guofa , Qiu Chong , Cheng Bitao , Wang Wenbo 

TITLE=On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

JOURNAL=Frontiers in Physics

VOLUME=Volume 11 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1185846

DOI=10.3389/fphy.2023.1185846

ISSN=2296-424X

ABSTRACT=In this paper, we consider the nonexistence and existence of solutions for a generalized quasilinear Schr\"{o}dinger equation with a Kirchhoff-type perturbation. When the nonlinearity $h(u)$ is critical or supercritical growth at infnity, the nonexistence result for quasilinear Schr\"{o}dinger equation is proved via Poho\v{z}aev identity. If $h(u)$ is asymptotically cubic growth at infinity, the existence of positive radial solutions for quasilinear Schr\"{o}dinger 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 $0$.