Spectrum, bifurcation and hypersurfaces of prescribed k-th mean curvature in Minkowski space

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-11-10 DOI:10.3233/asy-231877

Guowei Dai, Zhitao Zhang

引用次数: 0

Abstract

By bifurcation and topological methods, we study the existence/nonexistence and multiplicity of one-sign or nodal solutions of the following k-th mean curvature problem in Minkowski spacetime r N − k v ′ 1 − v ′ 2 k ′ = λ N C N k r N − 1 H k ( r , v ) in ( 0 , R ) , | v ′ | < 1 in ( 0 , R ) , v ′ ( 0 ) = v ( R ) = 0 . As a previous step, we investigate the spectral structure of its linearized problem at zero. Moreover, we also obtain a priori bounds and the asymptotic behaviors of solutions with respect to λ.

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闵可夫斯基空间中规定k次平均曲率的谱、分岔和超曲面

利用分岔方法和拓扑方法，研究了Minkowski时空r N−k v ' 1−v ' 2 k ' = λ N C N k r N−1 H k (r, v) in (0, r)， | v ' <中k-平均曲率问题的一符号或节点解的存在性/不存在性和多重性;1 in (0, R) v ' (0) = v (R) = 0。作为前一步，我们研究了它在零处线性化问题的谱结构。此外，我们还得到了关于λ的先验界和解的渐近性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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