Pub Date : 2024-09-12DOI: 10.1080/17476933.2024.2375562
Haiyang He, Xiao Li
In this paper, our purpose is to study the following Hénon-type Bi-harmonic Choquard equation (1) Δ2u=∫RN|x|α|y|αup(y)|x−y|N−μdyup−1,inRN, where α>0,0<μ
{"title":"Liouville theorem for Hénon-type bi-harmonic Choquard equation in","authors":"Haiyang He, Xiao Li","doi":"10.1080/17476933.2024.2375562","DOIUrl":"https://doi.org/10.1080/17476933.2024.2375562","url":null,"abstract":"In this paper, our purpose is to study the following Hénon-type Bi-harmonic Choquard equation (1) Δ2u=∫RN|x|α|y|αup(y)|x−y|N−μdyup−1,inRN, where α>0,0<μ<N. Let N = 5 and 2<p<5+2α+μ, we will show...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"21 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142250872","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 : 2024-09-05DOI: 10.1080/17476933.2024.2372100
Xin Du, Chun-Lei Tang
In this paper, we consider the quasilinear Schrödinger–Poisson system {−Δu+V(x)u+ϕu−[Δ(1+u2)1/2]u2(1+u2)1/2=f(u)inR3,−Δϕ=u2inR3, where V is a given coercive potential and the nonlinearity include...
在本文中，我们考虑了准线性薛定谔-泊松系统 {-Δu+V(x)u+ϕu-[Δ(1+u2)1/2]u2(1+u2)1/2=f(u)inR3,-Δϕ=u2inR3, 其中 V 是给定的强制势，非线性包括...
{"title":"Existence and multiplicity of sign-changing solutions for quasilinear Schrödinger–Poisson system","authors":"Xin Du, Chun-Lei Tang","doi":"10.1080/17476933.2024.2372100","DOIUrl":"https://doi.org/10.1080/17476933.2024.2372100","url":null,"abstract":"In this paper, we consider the quasilinear Schrödinger–Poisson system {−Δu+V(x)u+ϕu−[Δ(1+u2)1/2]u2(1+u2)1/2=f(u)inR3,−Δϕ=u2inR3, where V is a given coercive potential and the nonlinearity include...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"11 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251203","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}
In this paper, we investigate the existence of solution to the fractional p-Laplacian equation (−Δ)psu+λ|u|p−2u=f(u)in RN,N≥2,u∈Ws,p(RN), satisfying the normalization constraint ∫RN|u|pdx=cp, whe...
{"title":"Normalized solutions for the fractional P-Laplacian equation with exponential critical growth","authors":"Ling Huang, Hangxin Wen, Jianjun Zhang, Xuexiu Zhong","doi":"10.1080/17476933.2024.2394876","DOIUrl":"https://doi.org/10.1080/17476933.2024.2394876","url":null,"abstract":"In this paper, we investigate the existence of solution to the fractional p-Laplacian equation (−Δ)psu+λ|u|p−2u=f(u)in RN,N≥2,u∈Ws,p(RN), satisfying the normalization constraint ∫RN|u|pdx=cp, whe...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268686","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}
The purpose of this paper is to study the Liouville property for the Lane–Emden equation involving the regional fractional Laplacian (−Δ)Ωsu+Vu=h1up+h2in Ω,u=0on ∂Ω, where s∈(0,1), p>0, h1,h2 are...
本文旨在研究涉及区域分数拉普拉奇（-Δ）Ωsu+Vu=h1up+h2 in Ω,u=0 on ∂Ω的Lane-Emden方程的Liouville性质，其中s∈(0,1), p>0, h1,h2为...
{"title":"Liouville theorem of the regional fractional Lane–Emden equations","authors":"Ying Wang, Yanqing Sun, Hongxing Chen, Hichem Hajaiej","doi":"10.1080/17476933.2024.2394878","DOIUrl":"https://doi.org/10.1080/17476933.2024.2394878","url":null,"abstract":"The purpose of this paper is to study the Liouville property for the Lane–Emden equation involving the regional fractional Laplacian (−Δ)Ωsu+Vu=h1up+h2in Ω,u=0on ∂Ω, where s∈(0,1), p>0, h1,h2 are...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"7 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209161","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 : 2024-08-21DOI: 10.1080/17476933.2024.2350958
Hamza El-Houari, Hicham Moussa, Hajar Sabiki
In this study, we thoroughly examine a specific type of complex mathematical problems involving a fractional ψκ,y(⋅)-Laplacian operator and a Choquard-logarithmic nonlinearity, combined with a real...
{"title":"Fractional Musielak spaces: study of nonlocal elliptic problem with Choquard-logarithmic nonlinearity","authors":"Hamza El-Houari, Hicham Moussa, Hajar Sabiki","doi":"10.1080/17476933.2024.2350958","DOIUrl":"https://doi.org/10.1080/17476933.2024.2350958","url":null,"abstract":"In this study, we thoroughly examine a specific type of complex mathematical problems involving a fractional ψκ,y(⋅)-Laplacian operator and a Choquard-logarithmic nonlinearity, combined with a real...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209163","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 : 2024-08-15DOI: 10.1080/17476933.2024.2382791
Kheireddine Biroud
In this work we deal with the nonlocal elliptic system: (S){(−Δ)s1u=θvqu1−θin Ω,(−Δ)s2v=qvq−1uθin Ω,u=v=0in RN∖Ω,u,v>0in Ω, where Ω⊂RN is a bounded regular domain (C2 is sufficient), N>2s2, s1,s2...
在这项工作中，我们处理非局部椭圆系统：(S){(-Δ)s1u=θvqu1-θ in Ω,(-Δ)s2v=qvq-1uθ in Ω,u=v=0 in RN∖Ω,u,v>0 in Ω，其中 Ω⊂RN 是有界正则域（C2 即可），N>2s2，s1,s2...
{"title":"A nonlocal elliptic system with nonlinear singular terms","authors":"Kheireddine Biroud","doi":"10.1080/17476933.2024.2382791","DOIUrl":"https://doi.org/10.1080/17476933.2024.2382791","url":null,"abstract":"In this work we deal with the nonlocal elliptic system: (S){(−Δ)s1u=θvqu1−θin Ω,(−Δ)s2v=qvq−1uθin Ω,u=v=0in RN∖Ω,u,v>0in Ω, where Ω⊂RN is a bounded regular domain (C2 is sufficient), N>2s2, s1,s2...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"11 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209164","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 : 2024-08-13DOI: 10.1080/17476933.2024.2384485
Mohamed Jleli, Bessem Samet, Calogero Vetro
Let Δk be the Dunkl generalized Laplacian operator associated to a root system R of RN and a nonnegative multiplicity function k defined on R and invariant by the finite reflection group W. In this...
让 Δk 是与 RN 的根系 R 和定义在 R 上且通过有限反射群 W 不变的非负乘法函数 k 相关联的 Dunkl 广义拉普拉斯算子。
{"title":"Liouville-type results for semilinear inequalities involving the Dunkl Laplacian operator","authors":"Mohamed Jleli, Bessem Samet, Calogero Vetro","doi":"10.1080/17476933.2024.2384485","DOIUrl":"https://doi.org/10.1080/17476933.2024.2384485","url":null,"abstract":"Let Δk be the Dunkl generalized Laplacian operator associated to a root system R of RN and a nonnegative multiplicity function k defined on R and invariant by the finite reflection group W. In this...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"19 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209165","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 : 2024-08-06DOI: 10.1080/17476933.2024.2364645
A. Bentrad
This paper deals with the solutions for some classes of non-elliptic Cauchy–Riemann type systems with singular coefficients.We give an explicit representation of the solutions and study their singu...
本文讨论了一些具有奇异系数的非椭圆考奇-黎曼型系统的解。
{"title":"Exact solutions for some classes of non-elliptic Cauchy–Riemann type systems with singular coefficients","authors":"A. Bentrad","doi":"10.1080/17476933.2024.2364645","DOIUrl":"https://doi.org/10.1080/17476933.2024.2364645","url":null,"abstract":"This paper deals with the solutions for some classes of non-elliptic Cauchy–Riemann type systems with singular coefficients.We give an explicit representation of the solutions and study their singu...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947461","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 : 2024-08-01DOI: 10.1080/17476933.2024.2384482
Tesfa Mengestie
We describe the conditions under which the superposition operator maps one harmonic Fock space into another. We further proved that all superposition operators on the spaces are both bounded and gl...
{"title":"The nonlinear superposition operator on harmonic fock spaces","authors":"Tesfa Mengestie","doi":"10.1080/17476933.2024.2384482","DOIUrl":"https://doi.org/10.1080/17476933.2024.2384482","url":null,"abstract":"We describe the conditions under which the superposition operator maps one harmonic Fock space into another. We further proved that all superposition operators on the spaces are both bounded and gl...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"11 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947462","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 : 2024-07-30DOI: 10.1080/17476933.2024.2384478
Maria Trybuła
The Hadamard product of two holomorphic functions given by Taylor series ∑αaαzα and ∑αbαzα, defined on neighborhoods Ω1 and Ω2 of the origin, is the function whose Taylor series is ∑αaαbαzα. For n=...
{"title":"On the Hadamard multiplication theorem in ℂn","authors":"Maria Trybuła","doi":"10.1080/17476933.2024.2384478","DOIUrl":"https://doi.org/10.1080/17476933.2024.2384478","url":null,"abstract":"The Hadamard product of two holomorphic functions given by Taylor series ∑αaαzα and ∑αbαzα, defined on neighborhoods Ω1 and Ω2 of the origin, is the function whose Taylor series is ∑αaαbαzα. For n=...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"29 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866059","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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