{"title":"Multibump Solutions for Critical Choquard Equation","authors":"Jiankang Xia, Xu Zhang","doi":"10.1137/23m1581820","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3832-3860, June 2024. <br/> Abstract. We are concerned with the critical Choquard equation [math] where [math], [math] is the Riesz potential with order [math], and the exponent [math] is critical with respect to the Hardy–Littlewood–Sobolev inequality. By combining the variational gluing method and a penalization technique, for every [math], we prove the existence of infinitely many [math]-bump positive solutions for this nonlocal equation exhibiting a polynomial decay at infinity if the potential [math] is periodic in one of its variables and permits a global maxima with a fast decay rate near the maximum point. Our results demonstrate the nonlocal features of the Choquard equation and do not depend on the uniqueness or nondegeneracy property of positive solutions, which is in contrast to the results of the local Yamabe equation.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1581820","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3832-3860, June 2024. Abstract. We are concerned with the critical Choquard equation [math] where [math], [math] is the Riesz potential with order [math], and the exponent [math] is critical with respect to the Hardy–Littlewood–Sobolev inequality. By combining the variational gluing method and a penalization technique, for every [math], we prove the existence of infinitely many [math]-bump positive solutions for this nonlocal equation exhibiting a polynomial decay at infinity if the potential [math] is periodic in one of its variables and permits a global maxima with a fast decay rate near the maximum point. Our results demonstrate the nonlocal features of the Choquard equation and do not depend on the uniqueness or nondegeneracy property of positive solutions, which is in contrast to the results of the local Yamabe equation.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere.
Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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