Pub Date : 2023-12-14DOI: 10.1080/17476933.2023.2289528
G.C. Anthal, J. Giacomoni, K. Sreenadh
In this article, we study a class of elliptic problems involving both local and nonlocal operators with different orders and a singular nonlinearity in combination with critical Hartree type nonlin...
{"title":"Mixed local and nonlocal elliptic equation with singular and critical Choquard nonlinearity","authors":"G.C. Anthal, J. Giacomoni, K. Sreenadh","doi":"10.1080/17476933.2023.2289528","DOIUrl":"https://doi.org/10.1080/17476933.2023.2289528","url":null,"abstract":"In this article, we study a class of elliptic problems involving both local and nonlocal operators with different orders and a singular nonlinearity in combination with critical Hartree type nonlin...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138691282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.1080/17476933.2023.2289498
Junmin Han, Xi Wu, Di Zhao
In this paper, we consider a Kohn–Nirenberg type domain Ω={(z1,…,zn)∈Cn:Rezn+∑j=1n−1(|zj|p+Kj|zj|p−qRezjq+Lj|zj|p−qImzjq)<0} and discuss the existence of supporting surface and peak function at the...
{"title":"A Kohn–Nirenberg type domain in Cn","authors":"Junmin Han, Xi Wu, Di Zhao","doi":"10.1080/17476933.2023.2289498","DOIUrl":"https://doi.org/10.1080/17476933.2023.2289498","url":null,"abstract":"In this paper, we consider a Kohn–Nirenberg type domain Ω={(z1,…,zn)∈Cn:Rezn+∑j=1n−1(|zj|p+Kj|zj|p−qRezjq+Lj|zj|p−qImzjq)<0} and discuss the existence of supporting surface and peak function at the...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138690978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.1080/17476933.2023.2289472
Ritu Raj, Bidhan Chandra Sardar
This article introduces the boundary optimal control problem in an N-dimensional domain governed by the stationary Stokes equations. Controls are applied to the states through Neumann data on the b...
本文介绍了受静止斯托克斯方程支配的 N 维域中的边界最优控制问题。控制是通过边界上的诺伊曼数据对状态进行控制。
{"title":"Homogenization and corrector result of optimal control problem for Stokes system","authors":"Ritu Raj, Bidhan Chandra Sardar","doi":"10.1080/17476933.2023.2289472","DOIUrl":"https://doi.org/10.1080/17476933.2023.2289472","url":null,"abstract":"This article introduces the boundary optimal control problem in an N-dimensional domain governed by the stationary Stokes equations. Controls are applied to the states through Neumann data on the b...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138691101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-03DOI: 10.1080/17476933.2023.2287013
Abdelwahed Chrih, Youssef Khelifi
In this article, we introduce a new generalized squeezing function defined on bounded domains in Cn and we describe its properties. We compare our generalized squeezing function with the squeezing ...
本文引入了在Cn有界域上定义的一个新的广义压缩函数，并描述了它的性质。我们将我们的广义压缩函数与
{"title":"A generalization of squeezing function","authors":"Abdelwahed Chrih, Youssef Khelifi","doi":"10.1080/17476933.2023.2287013","DOIUrl":"https://doi.org/10.1080/17476933.2023.2287013","url":null,"abstract":"In this article, we introduce a new generalized squeezing function defined on bounded domains in Cn and we describe its properties. We compare our generalized squeezing function with the squeezing ...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-01DOI: 10.1080/17476933.2023.2287007
Abdelhakim Sahbani
In this paper, we study by using variational methods, mountain pass theorem, Z2-mountain pass theorem combined with the theory of the generalized Lebesgue Sobolev spaces, the existence and multipli...
{"title":"Infinitely many solutions for problems involving -Laplacian and -biharmonic operators","authors":"Abdelhakim Sahbani","doi":"10.1080/17476933.2023.2287007","DOIUrl":"https://doi.org/10.1080/17476933.2023.2287007","url":null,"abstract":"In this paper, we study by using variational methods, mountain pass theorem, Z2-mountain pass theorem combined with the theory of the generalized Lebesgue Sobolev spaces, the existence and multipli...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-30DOI: 10.1080/17476933.2023.2283879
Luis O. Silva, Julio H. Toloza
A de Branges space B is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map F(z)↦F(−z). Let KB(z,w) be the reproduci...
如果A de Branges空间B的常数属于它的关联函数空间，则它是正则的;如果它在映射F(z)∑F(−z)下是等距不变的，则它是对称的。设KB(z,w)为复现…
{"title":"Oversampling on a class of symmetric regular de Branges spaces","authors":"Luis O. Silva, Julio H. Toloza","doi":"10.1080/17476933.2023.2283879","DOIUrl":"https://doi.org/10.1080/17476933.2023.2283879","url":null,"abstract":"A de Branges space B is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map F(z)↦F(−z). Let KB(z,w) be the reproduci...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-29DOI: 10.1080/17476933.2023.2280966
J.C. de Albuquerque, J.L. Santos
This paper focuses on the following class of fractional magnetic Schrödinger equations: (−Δ)Asu+V(x)u=g(|u|2)u+λ|u|q−2u,in RN, where (−Δ)As is the fractional magnetic Laplacian, A:RN→RN is the ma...
{"title":"Fractional magnetic Schrödinger equations with potential vanishing at infinity and supercritical exponents","authors":"J.C. de Albuquerque, J.L. Santos","doi":"10.1080/17476933.2023.2280966","DOIUrl":"https://doi.org/10.1080/17476933.2023.2280966","url":null,"abstract":"This paper focuses on the following class of fractional magnetic Schrödinger equations: (−Δ)Asu+V(x)u=g(|u|2)u+λ|u|q−2u,in RN, where (−Δ)As is the fractional magnetic Laplacian, A:RN→RN is the ma...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-20DOI: 10.1080/17476933.2023.2280955
H. P. Bueno, O. H. Miyagaki, A. L. Vieira
We prove the existence of infinitely many radially symmetric solutions to the problem (−Δp)su=g(u)inRN,u∈Ws,p(RN), where s∈(0,1), 2≤p<∞, sp≤N, 2≤N∈N and (−Δp)s is the fractional p-Laplacian opera...
{"title":"Multiplicity of solutions for a scalar field equation involving a fractional p-Laplacian with general nonlinearity","authors":"H. P. Bueno, O. H. Miyagaki, A. L. Vieira","doi":"10.1080/17476933.2023.2280955","DOIUrl":"https://doi.org/10.1080/17476933.2023.2280955","url":null,"abstract":"We prove the existence of infinitely many radially symmetric solutions to the problem (−Δp)su=g(u)inRN,u∈Ws,p(RN), where s∈(0,1), 2≤p<∞, sp≤N, 2≤N∈N and (−Δp)s is the fractional p-Laplacian opera...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-14DOI: 10.1080/17476933.2023.2280958
Yi C. Huang, Jian-Yang Zhang
AbstractIn this paper, we present a simple direct proof of an integration lemma due to Barsegian, Sergeev and Montes-Rodrigues, and extend to rational functions their upper estimates on the total length of Gamma-lines in complex plane.KEYWORDS: Gamma-lineslevel setsrational functionsmeromorphic functionsAMS SUBJECT CLASSIFICATIONS: Primary 30C10Secondary 11C08 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingResearch of the authors is supported by the National NSF grant of China (no. 11801274). YCH thanks Professor Barsegian for helpful and encouraging comments.
{"title":"On the total length of Gamma-lines for rational functions","authors":"Yi C. Huang, Jian-Yang Zhang","doi":"10.1080/17476933.2023.2280958","DOIUrl":"https://doi.org/10.1080/17476933.2023.2280958","url":null,"abstract":"AbstractIn this paper, we present a simple direct proof of an integration lemma due to Barsegian, Sergeev and Montes-Rodrigues, and extend to rational functions their upper estimates on the total length of Gamma-lines in complex plane.KEYWORDS: Gamma-lineslevel setsrational functionsmeromorphic functionsAMS SUBJECT CLASSIFICATIONS: Primary 30C10Secondary 11C08 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingResearch of the authors is supported by the National NSF grant of China (no. 11801274). YCH thanks Professor Barsegian for helpful and encouraging comments.","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-05DOI: 10.1080/17476933.2023.2270910
B. Y. Irgashev
AbstractIn this article, by the similarity method, self-similar solutions of higher-order equations with constant and variable coefficients are constructed. Self-similar solutions are expressed in terms of generalized hypergeometric functions. The examples show how the fundamental solutions of known equations can be expressed through the particular solutions we have constructed.Keywords: High-order equationmultiple characteristicsfundamental solutionsimilarity solutiongeneralised hypergeometric functiondegenerationAMS Subject Classification: 35C06 Disclosure statementNo potential conflict of interest was reported by the author(s).
{"title":"Application of hypergeometric functions to the construction of particular solutions","authors":"B. Y. Irgashev","doi":"10.1080/17476933.2023.2270910","DOIUrl":"https://doi.org/10.1080/17476933.2023.2270910","url":null,"abstract":"AbstractIn this article, by the similarity method, self-similar solutions of higher-order equations with constant and variable coefficients are constructed. Self-similar solutions are expressed in terms of generalized hypergeometric functions. The examples show how the fundamental solutions of known equations can be expressed through the particular solutions we have constructed.Keywords: High-order equationmultiple characteristicsfundamental solutionsimilarity solutiongeneralised hypergeometric functiondegenerationAMS Subject Classification: 35C06 Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135725200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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