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

Guofa Li; Chong Qiu; Bitao Cheng; Wenbo Wang

doi:10.3389/fphy.2023.1185846

Frontiers in Physics (May 2023)

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

Guofa Li,
Chong Qiu,
Bitao Cheng,
Wenbo Wang

Affiliations

Guofa Li: Key Laboratory of Analytical Mathematics and Intelligent Computing for Yunnan Provincial, Department of Education and College of Mathematics and Statistics, Qujing Normal University, Qujing, China
Chong Qiu: Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, China
Bitao Cheng: Key Laboratory of Analytical Mathematics and Intelligent Computing for Yunnan Provincial, Department of Education and College of Mathematics and Statistics, Qujing Normal University, Qujing, China
Wenbo Wang: Department of Mathematics and Statistics, Yunnan University, Kunming, China

DOI: https://doi.org/10.3389/fphy.2023.1185846
Journal volume & issue: Vol. 11

Abstract

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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 h(u) shows critical or supercritical growth at infinity, the non-existence result for a quasilinear Schrödinger equation is proved via the Pohožaev identity. If h(u) shows asymptotically cubic growth at infinity, the existence of positive radial solutions for the quasilinear Schrödinger 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.

Published in Frontiers in Physics

ISSN: 2296-424X (Online)
Publisher: Frontiers Media S.A.
Country of publisher: Switzerland
LCC subjects: Science: Physics
Website: https://www.frontiersin.org/journals/physics

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