{"title":"强不定Choquard方程的谱间隙分岔","authors":"Huxiao Luo, B. Ruf, C. Tarsi","doi":"10.1142/s0219199723500013","DOIUrl":null,"url":null,"abstract":": We consider the semilinear elliptic equations where I α is a Riesz potential, p ∈ ( N + αN , N + α N − 2 ), N ≥ 3, and V is continuous periodic. We assume that 0 lies in the spectral gap ( a, b ) of − ∆ + V . We prove the existence of infinitely many geometrically distinct solutions in H 1 ( R N ) for each λ ∈ ( a, b ), which bifurcate from b if N + αN < p < 1 + 2+ αN . Moreover, b is the unique gap-bifurcation point (from zero) in [ a, b ]. When λ = a , we find infinitely many geometrically distinct solutions in H 2 loc ( R N ). Final remarks are given about the eventual occurrence of a bifurcation from infinity in λ = a . 35Q55, 47J35.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Bifurcation into spectral gaps for strongly indefinite Choquard equations\",\"authors\":\"Huxiao Luo, B. Ruf, C. Tarsi\",\"doi\":\"10.1142/s0219199723500013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": We consider the semilinear elliptic equations where I α is a Riesz potential, p ∈ ( N + αN , N + α N − 2 ), N ≥ 3, and V is continuous periodic. We assume that 0 lies in the spectral gap ( a, b ) of − ∆ + V . We prove the existence of infinitely many geometrically distinct solutions in H 1 ( R N ) for each λ ∈ ( a, b ), which bifurcate from b if N + αN < p < 1 + 2+ αN . Moreover, b is the unique gap-bifurcation point (from zero) in [ a, b ]. When λ = a , we find infinitely many geometrically distinct solutions in H 2 loc ( R N ). Final remarks are given about the eventual occurrence of a bifurcation from infinity in λ = a . 35Q55, 47J35.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2022-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219199723500013\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219199723500013","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Bifurcation into spectral gaps for strongly indefinite Choquard equations
: We consider the semilinear elliptic equations where I α is a Riesz potential, p ∈ ( N + αN , N + α N − 2 ), N ≥ 3, and V is continuous periodic. We assume that 0 lies in the spectral gap ( a, b ) of − ∆ + V . We prove the existence of infinitely many geometrically distinct solutions in H 1 ( R N ) for each λ ∈ ( a, b ), which bifurcate from b if N + αN < p < 1 + 2+ αN . Moreover, b is the unique gap-bifurcation point (from zero) in [ a, b ]. When λ = a , we find infinitely many geometrically distinct solutions in H 2 loc ( R N ). Final remarks are given about the eventual occurrence of a bifurcation from infinity in λ = a . 35Q55, 47J35.
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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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