{"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":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2000,"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\":50660,\"journal\":{\"name\":\"Communications in Contemporary Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Contemporary Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219199723500013\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Contemporary Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219199723500013","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","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.
期刊介绍：
With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.
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