Pub Date : 2023-09-03DOI: 10.1080/17476933.2023.2250732
Siham Boukarabila, Ana Primo, Abdelbadie Younes
{"title":"Singular elliptic problem with super-quadratic growth in the gradient","authors":"Siham Boukarabila, Ana Primo, Abdelbadie Younes","doi":"10.1080/17476933.2023.2250732","DOIUrl":"https://doi.org/10.1080/17476933.2023.2250732","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45012752","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 : 2023-08-30DOI: 10.1080/17476933.2023.2250984
A. Harrabi, M. K. Hamdani, A. Fiscella
AbstractIn this paper, we prove the existence of infinitely many solutions for a class of quasilinear elliptic m-polyharmonic Kirchhoff equations where the nonlinear function has a quasicritical growth at infinity and without assuming the Ambrosetti and Rabinowitz type condition. The new aspect consists in employing the notion of a Schauder basis to verify the geometry of the symmetric mountain pass theorem. Furthermore, we introduce a positive quantity λM similar to the first eigenvalue of the m-polyharmonic operator to find a mountain pass solution, and also to discuss the sublinear case under large growth conditions at infinity and at zero. Our results are an improvement and generalization of the corresponding results obtained by Colasuonno-Pucci (Nonlinear Analysis: Theory, Methods and Applications, 2011) and Bae-Kim (Mathematical Methods in the Applied Sciences, 2020).Keywords: m-Polyharmonic operatorPalais-Smale conditionsymmetric mountain pass theoremschauder basisKrasnoselskii genus theoryKirchhoff equationsCOMMUNICATED BY: A. MezianiAMS Subject Classifications: Primary: 35J5535J65Secondary: 35B65 Disclosure statementNo potential conflict of interest was reported by the author(s).Correction StatementThis article has been republished with minor changes. These changes do not impact the academic content of the article.Notes1 More precisely, Pj are uniformly bounded, that is there exists C>0 such that ‖Pj(z)‖≤C‖z‖ for each j∈N∗ and all z∈W0r,m(Ω) (see [Citation24, Citation26])Additional informationFundingA. Harrabi gratefully acknowledge the approval and the support of this research study by the grant no. SCIA-2022-11-1398 from the Deanship of Scientific Research at Northern Border University, Arar, K.S.A. M. K. Hamdani was supported by the Tunisian Military Research Center for Science and Technology Laboratory LR19DN01. M.K. Hamdani expresses his deepest gratitude to the Military Aeronautical Specialities School, Sfax (ESA) for providing an excellent atmosphere for work. A. Fiscella is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). A. Fiscella realized the manuscript within the auspices of the INdAM-GNAMPA project titled 'Equazioni differenziali alle derivate parziali in fenomeni non lineari' (CUP_E55F22000270001) and of the FAPESP Thematic Project titled 'Systems and partial differential equations' (2019/02512-5). The authors wish to thank Professors Dong Ye and Nguyen Thanh Chung for stimulating discussions on the subject.
{"title":"Existence and multiplicity of solutions for <i>m</i>-polyharmonic Kirchhoff problems without Ambrosetti–Rabinowitz conditions","authors":"A. Harrabi, M. K. Hamdani, A. Fiscella","doi":"10.1080/17476933.2023.2250984","DOIUrl":"https://doi.org/10.1080/17476933.2023.2250984","url":null,"abstract":"AbstractIn this paper, we prove the existence of infinitely many solutions for a class of quasilinear elliptic m-polyharmonic Kirchhoff equations where the nonlinear function has a quasicritical growth at infinity and without assuming the Ambrosetti and Rabinowitz type condition. The new aspect consists in employing the notion of a Schauder basis to verify the geometry of the symmetric mountain pass theorem. Furthermore, we introduce a positive quantity λM similar to the first eigenvalue of the m-polyharmonic operator to find a mountain pass solution, and also to discuss the sublinear case under large growth conditions at infinity and at zero. Our results are an improvement and generalization of the corresponding results obtained by Colasuonno-Pucci (Nonlinear Analysis: Theory, Methods and Applications, 2011) and Bae-Kim (Mathematical Methods in the Applied Sciences, 2020).Keywords: m-Polyharmonic operatorPalais-Smale conditionsymmetric mountain pass theoremschauder basisKrasnoselskii genus theoryKirchhoff equationsCOMMUNICATED BY: A. MezianiAMS Subject Classifications: Primary: 35J5535J65Secondary: 35B65 Disclosure statementNo potential conflict of interest was reported by the author(s).Correction StatementThis article has been republished with minor changes. These changes do not impact the academic content of the article.Notes1 More precisely, Pj are uniformly bounded, that is there exists C>0 such that ‖Pj(z)‖≤C‖z‖ for each j∈N∗ and all z∈W0r,m(Ω) (see [Citation24, Citation26])Additional informationFundingA. Harrabi gratefully acknowledge the approval and the support of this research study by the grant no. SCIA-2022-11-1398 from the Deanship of Scientific Research at Northern Border University, Arar, K.S.A. M. K. Hamdani was supported by the Tunisian Military Research Center for Science and Technology Laboratory LR19DN01. M.K. Hamdani expresses his deepest gratitude to the Military Aeronautical Specialities School, Sfax (ESA) for providing an excellent atmosphere for work. A. Fiscella is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). A. Fiscella realized the manuscript within the auspices of the INdAM-GNAMPA project titled 'Equazioni differenziali alle derivate parziali in fenomeni non lineari' (CUP_E55F22000270001) and of the FAPESP Thematic Project titled 'Systems and partial differential equations' (2019/02512-5). The authors wish to thank Professors Dong Ye and Nguyen Thanh Chung for stimulating discussions on the subject.","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136037373","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 : 2023-08-29DOI: 10.1080/17476933.2023.2246901
Na Liu, Tao Wang
{"title":"Infinitely many nodal solutions for a modified Kirchhoff type equation","authors":"Na Liu, Tao Wang","doi":"10.1080/17476933.2023.2246901","DOIUrl":"https://doi.org/10.1080/17476933.2023.2246901","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43181322","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 : 2023-08-27DOI: 10.1080/17476933.2023.2247991
R. E. Castillo
{"title":"A note on unique continuation of eigenfunctions for p-Laplacian operator in a bounded domain Ω in ℝn with a potential V in Lp(Ω)","authors":"R. E. Castillo","doi":"10.1080/17476933.2023.2247991","DOIUrl":"https://doi.org/10.1080/17476933.2023.2247991","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43821654","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 : 2023-08-27DOI: 10.1080/17476933.2023.2249405
Zhitao Guo
{"title":"Frequent hypercyclicity of the tensor products of composition operators on weighted Dirichlet spaces","authors":"Zhitao Guo","doi":"10.1080/17476933.2023.2249405","DOIUrl":"https://doi.org/10.1080/17476933.2023.2249405","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46034328","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 : 2023-08-23DOI: 10.1080/17476933.2023.2244437
Hamed Emkanpour, N. Taghizadeh
{"title":"Complex boundary value problems on a circular triangle","authors":"Hamed Emkanpour, N. Taghizadeh","doi":"10.1080/17476933.2023.2244437","DOIUrl":"https://doi.org/10.1080/17476933.2023.2244437","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47567255","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 : 2023-08-23DOI: 10.1080/17476933.2023.2249420
A. Sharma, A. Sharma
{"title":"Order bounded and compact sums of weighted composition-differentiation operators","authors":"A. Sharma, A. Sharma","doi":"10.1080/17476933.2023.2249420","DOIUrl":"https://doi.org/10.1080/17476933.2023.2249420","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42925210","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 : 2023-08-20DOI: 10.1080/17476933.2023.2247998
Kaushik Mohanta, J. Tyagi
We study the following version of Hardy-type inequality on a domain $Omega$ in a Riemannian manifold $(M,g)$: $$ int{Omega}|nabla u|_g^prho^alpha dV_g geq left(frac{|p-1+beta|}{p}right)^pint{Omega}frac{|u|^p|nabla rho|_g^p}{|rho|^p}rho^alpha dV_g +int{Omega} V|u|^prho^alpha dV_g, quad forall uin C_c^infty (Omega). $$ We provide sufficient conditions on $p, alpha, beta,rho$ and $V$ for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities on Riemannian manifolds. The functional setup covers a wide variety of particular cases, which are discussed briefly: for example, $mathbb{R}^N$ with $p
{"title":"Improved hardy inequalities on Riemannian manifolds","authors":"Kaushik Mohanta, J. Tyagi","doi":"10.1080/17476933.2023.2247998","DOIUrl":"https://doi.org/10.1080/17476933.2023.2247998","url":null,"abstract":"We study the following version of Hardy-type inequality on a domain $Omega$ in a Riemannian manifold $(M,g)$: $$ int{Omega}|nabla u|_g^prho^alpha dV_g geq left(frac{|p-1+beta|}{p}right)^pint{Omega}frac{|u|^p|nabla rho|_g^p}{|rho|^p}rho^alpha dV_g +int{Omega} V|u|^prho^alpha dV_g, quad forall uin C_c^infty (Omega). $$ We provide sufficient conditions on $p, alpha, beta,rho$ and $V$ for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities on Riemannian manifolds. The functional setup covers a wide variety of particular cases, which are discussed briefly: for example, $mathbb{R}^N$ with $p","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44419678","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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