Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-23 DOI:10.1186/s13661-023-01789-0

Kamal Ould Bouh

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引用次数: 0

Abstract

Abstract This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents $(S_{\pm \varepsilon}): \Delta ^{2}u-c_{n}\Delta u+d_{n}u = Ku^{ \frac{n+4}{n-4}\pm \varepsilon}$ ( S ± ε ) : Δ 2 u − c n Δ u + d n u = K u n + 4 n − 4 ± ε , $u>0$ u > 0 on $S^{n}$ S n , where $n\geq 5$ n ≥ 5 , ε is a small positive parameter and K is a smooth positive function on $S^{n}$ S n . We construct some solutions of $(S_{-\varepsilon})$ ( S − ε ) that blow up at one critical point of K . However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation $(S_{+\varepsilon})$ ( S + ε ) .

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球面上Paneitz问题近似解的存在性与不存在性

抽象非线性问题》这篇文章devoted to studying有点subcritical和supercritical exponents (S_ {pm \ varepsilon}美元):\ ^{2}三角洲三角洲u-c_ {n} \我^ d_ {n} u + u = {\ frac {n + 4} {n-4的pm \ varepsilon}美元(S±ε):Δ2−c nΔu + d u n K u = u n + 4−4±ε,u>美元;u > 0美元;0美元在S ^ {n} $ n, n \ geq美元哪里5 n≥5美元,ε是a small积极和K是一个流畅的积极功能参数on S ^ {n} $ n美元。我们构造的一些解决方案(S_美元{- \ varepsilon}) (S−美元ε)那吹起来at一号连接point of K。,但是,我们也证明a nonexistence single-peaked解决方案》的论点supercritical equation (S_美元{\ varepsilon})美元(S +ε)。

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.