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=11

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