{"title":"Ground state solutions for quasilinear Schrödinger equations with critical Berestycki–Lions nonlinearities","authors":"Jian-Xin Han, Ming-Chao Chen, Yan-Fang Xue","doi":"10.1007/s10986-024-09635-1","DOIUrl":null,"url":null,"abstract":"<p>We consider the quasilinear Schrödinger equation involving a general nonlinearity at critical growth. By using Jeanjean’s monotonicity trick and the Pohozaev identity we get the existence results that generalize an earlier work [H. Liu and L. Zhao, Existence results for quasilinear Schrödinger equations with a general nonlinearity, <i>Commun. Pure Appl. Anal.</i>, 19(6):3429–3444, 2020] about the subcritical case to the critical case.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lithuanian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10986-024-09635-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the quasilinear Schrödinger equation involving a general nonlinearity at critical growth. By using Jeanjean’s monotonicity trick and the Pohozaev identity we get the existence results that generalize an earlier work [H. Liu and L. Zhao, Existence results for quasilinear Schrödinger equations with a general nonlinearity, Commun. Pure Appl. Anal., 19(6):3429–3444, 2020] about the subcritical case to the critical case.
我们考虑的是涉及临界增长时一般非线性的准线性薛定谔方程。通过使用 Jeanjean 的单调性技巧和 Pohozaev 特性，我们得到了存在性结果，这些结果概括了早先的工作 [H. Liu and L. Zhao, Existence results for quasilinear Schrödinger equations with general nonlinearity at the critical growth]。Liu and L. Zhao, Existence results for quasilinear Schrödinger equations with a general nonlinearity, Commun. Pure Appl.纯应用分析，19(6):3429-3444, 2020]有关亚临界情况到临界情况的存在性结果。
期刊介绍：
The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics.
The scope of the journal includes but is not limited to:
Probability theory and statistics;
Differential equations (theory and numerical methods);
Number theory;
Financial and actuarial mathematics, econometrics.
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