Pub Date : 2024-04-12DOI: 10.1080/17476933.2024.2310228
Zhongyuan Liu, Ziying Liu, Wenhuan Xu
In this paper, we study the existence and nonexistence results to the Choquard equation −Δu=(∫RN|u(y)|2α∗|x−y|αdy)|u|2α∗−2u±|u|q−2uinRN, where 2α∗=2N−αN−2, 0<α
{"title":"On the Choquard equation with double critical Sobolev exponents in ℝN","authors":"Zhongyuan Liu, Ziying Liu, Wenhuan Xu","doi":"10.1080/17476933.2024.2310228","DOIUrl":"https://doi.org/10.1080/17476933.2024.2310228","url":null,"abstract":"In this paper, we study the existence and nonexistence results to the Choquard equation −Δu=(∫RN|u(y)|2α∗|x−y|αdy)|u|2α∗−2u±|u|q−2uinRN, where 2α∗=2N−αN−2, 0<α<N, 1<q≤2∗, 2∗=2NN−2, N≥3. We first ...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567738","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 : 2024-04-08DOI: 10.1080/17476933.2024.2332312
Yansheng Shen
In this paper, we consider the following fractional (p,q)-Laplacian equations with critical Hardy-Sobolev exponents {(−Δ)ps1u+(−Δ)qs2u=λ|u|r−2u+μ|u|ps1∗(α)−2u|x|αinΩ,u=0inRN∖Ω, where 0
{"title":"On a fractional (p,q)-Laplacian equation with critical nonlinearities","authors":"Yansheng Shen","doi":"10.1080/17476933.2024.2332312","DOIUrl":"https://doi.org/10.1080/17476933.2024.2332312","url":null,"abstract":"In this paper, we consider the following fractional (p,q)-Laplacian equations with critical Hardy-Sobolev exponents {(−Δ)ps1u+(−Δ)qs2u=λ|u|r−2u+μ|u|ps1∗(α)−2u|x|αinΩ,u=0inRN∖Ω, where 0<s2<s1<1<q<...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567990","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 : 2024-03-20DOI: 10.1080/17476933.2024.2326833
N. Verma, S. Sivaprasad Kumar
This paper presents several results concerning second and third-order differential subordination for the class Se∗:={f∈A:zf′(z)/f(z)≺ez}, which represents the class of starlike functions associated...
{"title":"Differential subordination of certain class of starlike functions","authors":"N. Verma, S. Sivaprasad Kumar","doi":"10.1080/17476933.2024.2326833","DOIUrl":"https://doi.org/10.1080/17476933.2024.2326833","url":null,"abstract":"This paper presents several results concerning second and third-order differential subordination for the class Se∗:={f∈A:zf′(z)/f(z)≺ez}, which represents the class of starlike functions associated...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140170588","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 : 2024-03-05DOI: 10.1080/17476933.2024.2321608
Imed Abid, Sami Baraket
In this paper, we investigate a fourth-order weighted equation of the form Δ(w(x)|Δu|N2−2Δu)=f(x,u) within the unit ball B of RN. Our focus lies on establishing the existence of solutions under the...
在本文中，我们研究了在 RN 的单位球 B 内形式为 Δ(w(x)|Δu|N2-2Δu)=f(x,u) 的四阶加权方程。我们的重点在于确定在...
{"title":"Ground states of biharmonic equations with logarithmic weights and critical exponential growth","authors":"Imed Abid, Sami Baraket","doi":"10.1080/17476933.2024.2321608","DOIUrl":"https://doi.org/10.1080/17476933.2024.2321608","url":null,"abstract":"In this paper, we investigate a fourth-order weighted equation of the form Δ(w(x)|Δu|N2−2Δu)=f(x,u) within the unit ball B of RN. Our focus lies on establishing the existence of solutions under the...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045290","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 : 2024-02-29DOI: 10.1080/17476933.2024.2321356
Shi-Yi Lan, Jia Zhang
Let Σ be any disjoint union of finitely many simple curves in the strip region. Based on the continuous dependence of dipolar Loewner chains and the pre-compactness of driving functions associated ...
{"title":"The dipolar Schramm-Loewner equation for finitely many slits","authors":"Shi-Yi Lan, Jia Zhang","doi":"10.1080/17476933.2024.2321356","DOIUrl":"https://doi.org/10.1080/17476933.2024.2321356","url":null,"abstract":"Let Σ be any disjoint union of finitely many simple curves in the strip region. Based on the continuous dependence of dipolar Loewner chains and the pre-compactness of driving functions associated ...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010710","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 : 2024-02-21DOI: 10.1080/17476933.2024.2310225
Debajyoti Choudhuri, Rana Alkhal, Kamel Saoudi
The aim of this work is to study the elliptic problem: (−Δp)su+|u|p−2u=μf(x,u)+λu−γ in Ω,u>0 in Ω,Npsu+α(x)|u|p−2u=0 in RN∖Ω, under some conditions on the nonlinearity f. Here 2≤p≤ps∗, μ,λ>0, 0
本文旨在研究非线性 f 的某些条件下的椭圆问题：(-Δp)su+|u|p-2u=μf(x,u)+λu-γ in Ω,u>0 in Ω,Npsu+α(x)|u|p-2u=0 in RN∖Ω。
{"title":"Existence of solution for a nonlocal elliptic problem with a Robin-type data","authors":"Debajyoti Choudhuri, Rana Alkhal, Kamel Saoudi","doi":"10.1080/17476933.2024.2310225","DOIUrl":"https://doi.org/10.1080/17476933.2024.2310225","url":null,"abstract":"The aim of this work is to study the elliptic problem: (−Δp)su+|u|p−2u=μf(x,u)+λu−γ in Ω,u>0 in Ω,Npsu+α(x)|u|p−2u=0 in RN∖Ω, under some conditions on the nonlinearity f. Here 2≤p≤ps∗, μ,λ>0, 0<s...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953424","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 : 2024-02-20DOI: 10.1080/17476933.2024.2316645
Xiumei Han, Zohreh Naghizadeh, Binlin Zhang
In this article, we study required conditions to guarantee the nonexistence and multiplicity of solutions for a fractional weighted (p,q)-Kirchhoff system by using variational techniques.
{"title":"Nonexistence and multiplicity results for a fractional weighted (p,q)-Kirchhoff system","authors":"Xiumei Han, Zohreh Naghizadeh, Binlin Zhang","doi":"10.1080/17476933.2024.2316645","DOIUrl":"https://doi.org/10.1080/17476933.2024.2316645","url":null,"abstract":"In this article, we study required conditions to guarantee the nonexistence and multiplicity of solutions for a fractional weighted (p,q)-Kirchhoff system by using variational techniques.","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923796","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 : 2024-02-14DOI: 10.1080/17476933.2023.2298834
Vasudevarao Allu, Himadri Halder
For α∈(0,∞), let BH,Ω(α) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω⊆C. In this article, we study coefficient estimates for harmonic α-Bloch mappings on a pr...
{"title":"Landau's theorem for harmonic Bloch functions on simply connected domains","authors":"Vasudevarao Allu, Himadri Halder","doi":"10.1080/17476933.2023.2298834","DOIUrl":"https://doi.org/10.1080/17476933.2023.2298834","url":null,"abstract":"For α∈(0,∞), let BH,Ω(α) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω⊆C. In this article, we study coefficient estimates for harmonic α-Bloch mappings on a pr...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139751470","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 : 2024-02-13DOI: 10.1080/17476933.2024.2310231
Liulan Li, Tao Qian, Shilin Wang
In this paper, we introduce a new member to the universal families, called universal quotient Blaschke product, which is a formal quotient of two formal infinite Blaschke products. A formal infinit...
{"title":"On universal quotient Blaschke products","authors":"Liulan Li, Tao Qian, Shilin Wang","doi":"10.1080/17476933.2024.2310231","DOIUrl":"https://doi.org/10.1080/17476933.2024.2310231","url":null,"abstract":"In this paper, we introduce a new member to the universal families, called universal quotient Blaschke product, which is a formal quotient of two formal infinite Blaschke products. A formal infinit...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773355","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 : 2024-02-12DOI: 10.1080/17476933.2024.2310227
Asma Amira Batahri, Ahmed Attar, Abdelrazek Dieb
The main purpose of this work is to study a non-local scalar field equation in bounded domains. More precisely we consider the semi-linear fractional elliptic problem: (−Δ)su=λup−1−um−1 in Ω,u>0 i...
这项工作的主要目的是研究有界域中的非局部标量场方程。更确切地说，我们考虑的是半线性分数椭圆问题：(-Δ)su=λup-1-um-1 in Ω,u>0 i...
{"title":"A non-local scalar field problem: existence, multiplicity and asymptotic behavior","authors":"Asma Amira Batahri, Ahmed Attar, Abdelrazek Dieb","doi":"10.1080/17476933.2024.2310227","DOIUrl":"https://doi.org/10.1080/17476933.2024.2310227","url":null,"abstract":"The main purpose of this work is to study a non-local scalar field equation in bounded domains. More precisely we consider the semi-linear fractional elliptic problem: (−Δ)su=λup−1−um−1 in Ω,u>0 i...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139751394","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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