Nguyen Van Thin, Pham Thi Thuy, Trinh Thi Diep Linh
{"title":"具有非局部Choquard反应和指数增长的(p, q)分数阶拉普拉斯方程解的存在性","authors":"Nguyen Van Thin, Pham Thi Thuy, Trinh Thi Diep Linh","doi":"10.1080/17476933.2023.2261004","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, we study the existence of weak solution to (p,q)-fractional Choquard equation in RN as follows Lpsu+Lqsu+V(x)(|u|p−2u+|u|q−2u)=(1|x|μ∗F(u))f(u), where 2≤Ns=p<q, 0≤μ<N, f has exponential growth. The function f and V are continuous which satisfy some suitable assumptions. In our best knowledge, sofar there is not any work about existence of weak solution to (p,q)-fractional Choquard equation with exponential growth. Our results are even new in the case (N,q)-Laplace equation which are complement the results of Fiscella and Pucci [(p,N) equations with critical exponential nonlinearities in RN. J Math Anal Appl. 2021;501(1), Article 123379].Keywords: Integrodifferential operatorsTrudinger–Moser inequalityfractional (p,q)-Laplacianmountain pass theoremvariational methodAMS Subject Classifications: Primary 35A1535A2335J3535J6035R11 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe author wishes to express thanks to the referee and editorial board for reading the manuscript very carefully and making some valuable suggestions and comments towards the improvement of the paper. The first author would like to thank Prof. Claudianor O. Alves for useful comments to improve the first version of this paper. The research results are supported by Ministry of Education and Training of Vietnam under project with the name ‘Some properties about solutions to differential equations, fractional partial differential equations’ and grant number B2023-TNA-14.","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of solution for the ( <i>p, q</i> )-fractional Laplacian equation with nonlocal Choquard reaction and exponential growth\",\"authors\":\"Nguyen Van Thin, Pham Thi Thuy, Trinh Thi Diep Linh\",\"doi\":\"10.1080/17476933.2023.2261004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractIn this paper, we study the existence of weak solution to (p,q)-fractional Choquard equation in RN as follows Lpsu+Lqsu+V(x)(|u|p−2u+|u|q−2u)=(1|x|μ∗F(u))f(u), where 2≤Ns=p<q, 0≤μ<N, f has exponential growth. The function f and V are continuous which satisfy some suitable assumptions. In our best knowledge, sofar there is not any work about existence of weak solution to (p,q)-fractional Choquard equation with exponential growth. Our results are even new in the case (N,q)-Laplace equation which are complement the results of Fiscella and Pucci [(p,N) equations with critical exponential nonlinearities in RN. J Math Anal Appl. 2021;501(1), Article 123379].Keywords: Integrodifferential operatorsTrudinger–Moser inequalityfractional (p,q)-Laplacianmountain pass theoremvariational methodAMS Subject Classifications: Primary 35A1535A2335J3535J6035R11 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe author wishes to express thanks to the referee and editorial board for reading the manuscript very carefully and making some valuable suggestions and comments towards the improvement of the paper. The first author would like to thank Prof. Claudianor O. Alves for useful comments to improve the first version of this paper. The research results are supported by Ministry of Education and Training of Vietnam under project with the name ‘Some properties about solutions to differential equations, fractional partial differential equations’ and grant number B2023-TNA-14.\",\"PeriodicalId\":51229,\"journal\":{\"name\":\"Complex Variables and Elliptic Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Variables and Elliptic Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/17476933.2023.2261004\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables and Elliptic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17476933.2023.2261004","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence of solution for the ( p, q )-fractional Laplacian equation with nonlocal Choquard reaction and exponential growth
AbstractIn this paper, we study the existence of weak solution to (p,q)-fractional Choquard equation in RN as follows Lpsu+Lqsu+V(x)(|u|p−2u+|u|q−2u)=(1|x|μ∗F(u))f(u), where 2≤Ns=p
期刊介绍：
Complex Variables and Elliptic Equations is devoted to complex variables and elliptic equations including linear and nonlinear equations and systems, function theoretical methods and applications, functional analytic, topological and variational methods, spectral theory, sub-elliptic and hypoelliptic equations, multivariable complex analysis and analysis on Lie groups, homogeneous spaces and CR-manifolds.
The Journal was formally published as Complex Variables Theory and Application.
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