Pub Date : 2024-04-28DOI: 10.1080/17476933.2024.2341768
Saber Ezzdini, Zagharide Zine El Abidine
We first derive sharp estimates on some potential functions on the half space R+n:={x=(x1,…,xn)∈Rn;xn>0}, n≥3. Then, these estimates are applied to demonstrate the existence of a positive solution...
{"title":"Estimating potential functions with applications to elliptic problems in half space","authors":"Saber Ezzdini, Zagharide Zine El Abidine","doi":"10.1080/17476933.2024.2341768","DOIUrl":"https://doi.org/10.1080/17476933.2024.2341768","url":null,"abstract":"We first derive sharp estimates on some potential functions on the half space R+n:={x=(x1,…,xn)∈Rn;xn>0}, n≥3. Then, these estimates are applied to demonstrate the existence of a positive solution...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"15 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140832006","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 : 2024-04-18DOI: 10.1080/17476933.2024.2336971
Wenjing Chen, Dongxue Feng
In this article, we establish the fractional version of concentration compactness principle to study the existence of solutions for the critical fractional p-Kirchhoff problem with magnetic field, ...
{"title":"Critical fractional p-Kirchhoff type problem with a generalized Choquard nonlinearity and magnetic field","authors":"Wenjing Chen, Dongxue Feng","doi":"10.1080/17476933.2024.2336971","DOIUrl":"https://doi.org/10.1080/17476933.2024.2336971","url":null,"abstract":"In this article, we establish the fractional version of concentration compactness principle to study the existence of solutions for the critical fractional p-Kirchhoff problem with magnetic field, ...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"235 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140629528","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 : 2024-04-18DOI: 10.1080/17476933.2024.2341770
Serkan Emek
Prescribing Robin boundary conditions for the iterated Poisson equation (∂z∂z¯)nw=f leads to Robin-n problems. Extending previous results by allowing an independent choice for the parameters αk,βk ...
{"title":"Iterated Robin problem, the case of various parameters","authors":"Serkan Emek","doi":"10.1080/17476933.2024.2341770","DOIUrl":"https://doi.org/10.1080/17476933.2024.2341770","url":null,"abstract":"Prescribing Robin boundary conditions for the iterated Poisson equation (∂z∂z¯)nw=f leads to Robin-n problems. Extending previous results by allowing an independent choice for the parameters αk,βk ...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140617826","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 : 2024-04-18DOI: 10.1080/17476933.2024.2338447
Arpita Kundu, Abhijit Banerjee
In 2023, Li–Du–Yi [Complex Var. Elliptic Equ., 68(10)2023, 1653–1677] proved that if two L-functions L1 and L2 in the extended Selberg class S# have positive degrees, satisfy the same functional eq...
{"title":"L-functions and meromorphic functions satisfying the same Riemann-type functional equation and sharing sets","authors":"Arpita Kundu, Abhijit Banerjee","doi":"10.1080/17476933.2024.2338447","DOIUrl":"https://doi.org/10.1080/17476933.2024.2338447","url":null,"abstract":"In 2023, Li–Du–Yi [Complex Var. Elliptic Equ., 68(10)2023, 1653–1677] proved that if two L-functions L1 and L2 in the extended Selberg class S# have positive degrees, satisfy the same functional eq...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"318 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140625711","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 : 2024-04-17DOI: 10.1080/17476933.2023.2299717
Ruyun Ma, Lijuan Yang
We are concerned with the existence of positive solutions for the quasilinear problem (P) {−Δpu=λK(|x|)f(u),x∈RN∖B(r0), g~1(u)u−a1∇u⋅x|x|→0,|x|→∞,g~2(u)u+a2∂u∂n=0,x∈∂B(r0), where Δps=div(|∇s|p−2...
{"title":"Global structure of positive solutions for a singular quasilinear elliptic problem","authors":"Ruyun Ma, Lijuan Yang","doi":"10.1080/17476933.2023.2299717","DOIUrl":"https://doi.org/10.1080/17476933.2023.2299717","url":null,"abstract":"We are concerned with the existence of positive solutions for the quasilinear problem (P) {−Δpu=λK(|x|)f(u),x∈RN∖B(r0), g~1(u)u−a1∇u⋅x|x|→0,|x|→∞,g~2(u)u+a2∂u∂n=0,x∈∂B(r0), where Δps=div(|∇s|p−2...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140617943","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 : 2024-04-14DOI: 10.1080/17476933.2024.2338436
Xin Bao, Ying Lv, Zeng-Qi Ou
In this article, we study a class of fractional Schrödinger equation (1) {(−Δ)su=λu+a(x)|u|p−2u,∫RN|u|2dx=c2,u∈Hs(RN), where N>2s, s∈(0,1) and p∈(2,2+4s/N),c>0. a(x)∈C(RN,R) is a positive potent...
{"title":"Normalized bound state solutions of fractional Schrödinger equations with general potential","authors":"Xin Bao, Ying Lv, Zeng-Qi Ou","doi":"10.1080/17476933.2024.2338436","DOIUrl":"https://doi.org/10.1080/17476933.2024.2338436","url":null,"abstract":"In this article, we study a class of fractional Schrödinger equation (1) {(−Δ)su=λu+a(x)|u|p−2u,∫RN|u|2dx=c2,u∈Hs(RN), where N>2s, s∈(0,1) and p∈(2,2+4s/N),c>0. a(x)∈C(RN,R) is a positive potent...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"254 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567950","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 : 2024-04-12DOI: 10.1080/17476933.2024.2337890
Tran Duc Ngoc, Si Duc Quang
The purpose of this paper is to establish a non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting an arbitrary family of hyp...
{"title":"Improvement of non-integrated defect relation for meromorphic maps from Kähler manifolds","authors":"Tran Duc Ngoc, Si Duc Quang","doi":"10.1080/17476933.2024.2337890","DOIUrl":"https://doi.org/10.1080/17476933.2024.2337890","url":null,"abstract":"The purpose of this paper is to establish a non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting an arbitrary family of hyp...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"75 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567940","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 : 2024-04-12DOI: 10.1080/17476933.2024.2337868
A. Razani
Here, we study the existence of a generalized and a strong generalized solutions of the Dirichlet competing Kohn–Spencer Laplacian with convection problem {−ΔHnp1u+μ1ΔHnq1u=f1(ξ,u,v,DHnu,DHnv),−ΔH...
{"title":"Competing Kohn–Spencer Laplacian systems with convection in non-isotropic Folland–Stein space","authors":"A. Razani","doi":"10.1080/17476933.2024.2337868","DOIUrl":"https://doi.org/10.1080/17476933.2024.2337868","url":null,"abstract":"Here, we study the existence of a generalized and a strong generalized solutions of the Dirichlet competing Kohn–Spencer Laplacian with convection problem {−ΔHnp1u+μ1ΔHnq1u=f1(ξ,u,v,DHnu,DHnv),−ΔH...","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"31 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567982","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 : 2024-04-12DOI: 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":"26 1","pages":""},"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":"32 1","pages":""},"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}
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