具有一般非线性的准线性薛定谔方程的归一化解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-16 DOI:10.3233/asy-241908

Ting Deng, Marco Squassina, Jianjun Zhang, Xuexiu Zhong

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引用次数: 0

摘要

我们关注的是以下准线性薛定谔方程的解-div(φ2(u)∇u)+φ(u)φ′(u)|∇u|2+λu=f(u),x∈RN，其中 N⩾3，c>；0，λ∈R 作为拉格朗日乘数出现，φ∈C1(R,R+)。允许非线性 f∈C(R,R) 在原点和无穷远处为质量次临界、质量临界和质量超临界。通过对偶方法、定点索引和全局分支方法，我们确定了上述问题的归一化解的存在性。这些结果将 L. Jeanjean、J. J. Zhang 和 X.X. Zhong 以前的结果扩展到了准线性情况。

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Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity

We are concerned with solutions of the following quasilinear Schrödinger equations −div(φ2(u)∇u)+φ(u)φ′(u)|∇u|2+λu=f(u),x∈RN with prescribed mass ∫RNu2dx=c, where N⩾3, c>0, λ∈R appears as the Lagrange multiplier and φ∈C1(R,R+). The nonlinearity f∈C(R,R) is allowed to be mass-subcritical, mass-critical and mass-supercritical at origin and infinity. Via a dual approach, the fixed point index and a global branch approach, we establish the existence of normalized solutions to the problem above. The results extend previous results by L. Jeanjean, J. J. Zhang and X.X. Zhong to the quasilinear case.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.