414
Views
89
CrossRef citations to date
0
Altmetric
Original Articles

Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity

&
Pages 469-495 | Received 01 Nov 2004, Accepted 01 Aug 2005, Published online: 01 Sep 2006

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (2)

Ting Guo, Xianhua Tang & Qi Zhang. (2022) Ground state solutions for Choquard equations with Hardy potentials and critical nonlinearity. Complex Variables and Elliptic Equations 67:7, pages 1579-1597.
Read now

Articles from other publishers (87)

Dongsheng Kang. (2024) Existence and properties of radial solutions to critical elliptic systems involving strongly coupled Hardy terms. Journal of Mathematical Analysis and Applications 536:2, pages 128252.
Crossref
Lucas C. F. Ferreira & Wender S. Lagoin. (2024) On a localization-in-frequency approach for a class of elliptic problems with singular boundary data. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, pages 1-35.
Crossref
Cristian Cazacu & Teodor Rugină. (2024) Best constants in bipolar L Hardy-type inequalities. Journal of Mathematical Analysis and Applications 530:1, pages 127635.
Crossref
Hongying Jiao, Shuhai Zhu & Jinguo Zhang. (2024) Existence of infinitely many solutions for critical sub-elliptic systems via genus theory. Communications in Analysis and Mechanics 16:2, pages 237-261.
Crossref
Lucas C. F. Ferreira & Wender S. Lagoin. (2023) An approach to elliptic equations with nonlinear gradient terms via a modulation framework. Bulletin of Mathematical Sciences 13:03.
Crossref
Dongsheng Kang. (2023) Radial solutions to critical elliptic systems involving p-Laplacian and different Hardy-type terms. Journal of Mathematical Analysis and Applications 526:1, pages 127326.
Crossref
Jinguo Zhang. (2022) Sub-elliptic problems with multiple critical Sobolev-Hardy exponents on Carnot groups. manuscripta mathematica 172:1-2, pages 1-29.
Crossref
Huyuan Chen & Xiaowei Chen. (2023) Dirichlet problems involving the Hardy-Leray operators with multiple polars. Advances in Nonlinear Analysis 12:1.
Crossref
Xiu Yang, Li-Lian Wang, Huiyuan Li & Changtao Sheng. (2023) Müntz Ball Polynomials and Müntz Spectral-Galerkin Methods for Singular Eigenvalue Problems. Journal of Scientific Computing 96:2.
Crossref
Jing Li. (2023) The weak solution of quasilinear System concerning Sobolev Critical conditions in R N . Journal of Physics: Conference Series 2525:1, pages 012015.
Crossref
Heilong Mi, Wen Zhang & Fangfang Liao. (2023) On nonlinear fractional Schrödinger equations with indefinite and Hardy potentials. Asymptotic Analysis 132:3-4, pages 305-330.
Crossref
Imen Metoui. (2022) Multipolar Hardy inequalities in $$L^{p}$$-spaces. Archiv der Mathematik 119:6, pages 601-611.
Crossref
Tianfang Wang, Wen Zhang & Jian Zhang. (2022) Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential. Asymptotic Analysis 130:1-2, pages 187-212.
Crossref
Peng Chen, Huimao Chen & Xianhua Tang. (2022) Ground States of K-component Coupled Nonlinear Schrödinger Equations with Inverse-square Potential. Chinese Annals of Mathematics, Series B 43:3, pages 319-342.
Crossref
Peng Chen, Xianhua Tang & Limin Zhang. (2022) Non-Nehari Manifold Method for Hamiltonian Elliptic System with Hardy Potential: Existence and Asymptotic Properties of Ground State Solution. The Journal of Geometric Analysis 32:2.
Crossref
Peng Chen & Xianhua Tang. (2022) Ground states for a system of nonlinear Schrödinger equations with singular potentials. Discrete and Continuous Dynamical Systems 42:10, pages 5105.
Crossref
Nestor F. Castañeda-Centurión & Lucas C.F. Ferreira. (2021) On singular elliptic boundary value problems via a harmonic analysis approach. Journal of Differential Equations 299, pages 402-428.
Crossref
Chen Jia, Zhimin Zhang & Lewei Zhao. (2021) Two-parameter localization for eigenfunctions of a Schrödinger operator in balls and spherical shells. Journal of Mathematical Physics 62:9.
Crossref
Hui Zhang, Fubiao Lin & Junying Cao. (2021) An Efficient Finite Element Method and Error Analysis for Schrödinger Equation with Inverse Square Singular Potential. Mathematical Problems in Engineering 2021, pages 1-9.
Crossref
Jinguo Zhang & Dengyun Yang. (2021) Critical Hardy-Sobolev Exponents Problem with Grushin Operator and Hardy-Type Singularity Terms. Acta Applicandae Mathematicae 172:1.
Crossref
Yubing Sui, Donghao Zhang, Junying Cao & Jun Zhang. (2020) An efficient finite element method and error analysis for eigenvalue problem of Schrödinger equation with an inverse square potential on spherical domain. Advances in Difference Equations 2020:1.
Crossref
Safia Benmansour, Sofiane Messirdi & Atika Matallah. (2020) Existence and nonexistence results for elliptic equations involving two critical singular nonlinearities at the same pole. Afrika Matematika 31:5-6, pages 949-957.
Crossref
Jinguo Zhang & Tsing‐San Hsu. (2020) Existence results for a fractional elliptic system with critical Sobolev‐Hardy exponents and concave‐convex nonlinearities. Mathematical Methods in the Applied Sciences 43:6, pages 3488-3512.
Crossref
Ting Guo & Xianhua Tang. (2020) Ground state solutions for nonlinear Choquard equations with inverse-square potentials1. Asymptotic Analysis 117:3-4, pages 141-160.
Crossref
Dongsheng Kang & Xiaonan Liu. (2020) Double critical surfaces of singular quasilinear elliptic systems. Journal of Mathematical Analysis and Applications 483:1, pages 123607.
Crossref
Veronica Felli, Debangana Mukherjee & Roberto Ognibene. (2020) On fractional multi-singular Schrödinger operators: Positivity and localization of binding. Journal of Functional Analysis 278:4, pages 108389.
Crossref
Jinguo Zhang & Tsing-San Hsu. (2019) Nonlocal Elliptic Systems Involving Critical Sobolev-Hardy Exponents and Concave-convex Nonlinearities. Taiwanese Journal of Mathematics 23:6.
Crossref
Jian Zhang & Wen Zhang. (2019) Existence and asymptotic behavior of ground states for Schrödinger systems with Hardy potential. Nonlinear Analysis 189, pages 111586.
Crossref
Zhenyu Guo & Wenming Zou. (2019) Positive ground state solutions for an elliptic system with Hardy-Sobolev critical exponent growth. Journal of Mathematical Physics 60:10.
Crossref
Dongsheng Kang, Mengru Liu & Liangshun Xu. (2019) Critical elliptic systems involving multiple strongly–coupled Hardy–type terms. Advances in Nonlinear Analysis 9:1, pages 866-881.
Crossref
Dongsheng Kang, Jing Li & Liangshun Xu. (2017) Existence and Nonexistence of Ground State Solutions to Singular Elliptic Systems. Bulletin of the Malaysian Mathematical Sciences Society 42:3, pages 859-884.
Crossref
Dongsheng Kang & Liangshun Xu. (2019) A critical surface for the solutions to singular elliptic systems. Journal of Mathematical Analysis and Applications 472:2, pages 2017-2033.
Crossref
M. Khiddi. (2019) The Existence of Positive Solution for Semilinear Elliptic Equations with Multiple an Inverse Square Potential and Hardy-Sobolev Critical Exponents. Abstract and Applied Analysis 2019, pages 1-10.
Crossref
Dongsheng Kang & Xiaonan Liu. (2019) A note on coupled elliptic systems involving different Hardy-type terms. Applied Mathematics Letters 89, pages 35-40.
Crossref
Dongsheng Kang & Xiaonan Liu. (2018) Singularities of solutions to elliptic systems involving different Hardy-type terms. Journal of Mathematical Analysis and Applications 468:2, pages 757-765.
Crossref
Marcello Lucia & S. Prashanth. (2018) Criticality theory for Schrödinger operators with singular potential. Journal of Differential Equations 265:8, pages 3400-3440.
Crossref
Suna Ma, Huiyuan Li & Zhimin Zhang. (2018) Efficient Spectral Methods for Some Singular Eigenvalue Problems. Journal of Scientific Computing 77:1, pages 657-688.
Crossref
Annunziata Loiudice. (2018) Local Behavior of Solutions to Subelliptic Problems with Hardy Potential on Carnot Groups. Mediterranean Journal of Mathematics 15:3.
Crossref
Dongsheng Kang & Liangshun Xu. (2018) Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities. Communications on Pure & Applied Analysis 17:2, pages 333-346.
Crossref
Dongsheng Kang & Ping Xiong. (2017) Existence and nonexistence results for critical biharmonic systems involving multiple singularities. Journal of Mathematical Analysis and Applications 452:1, pages 469-487.
Crossref
Zhenyu Guo. (2016) Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents. Mathematische Nachrichten 290:7, pages 1053-1065.
Crossref
Dongsheng Kang & Ping Xiong. (2017) Ground state solutions to biharmonic equations involving critical nonlinearities and multiple singular potentials. Applied Mathematics Letters 66, pages 9-15.
Crossref
Yanbin Sang. (2017) An exact estimate result for a semilinear equation with critical exponent and prescribed singularity. Journal of Mathematical Analysis and Applications 447:1, pages 128-153.
Crossref
Jian Zhang, Wen Zhang & Xianhua Tang. (2017) Ground state solutions for Hamiltonian elliptic system with inverse square potential. Discrete & Continuous Dynamical Systems - A 37:8, pages 4565-4583.
Crossref
Huiyuan Li & Zhimin Zhang. (2017) Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential. SIAM Journal on Scientific Computing 39:1, pages A114-A140.
Crossref
Dongsheng Kang & Yangguang Kang. (2015) Quasilinear Elliptic Systems Involving Critical Hardy–Sobolev and Sobolev Exponents. Bulletin of the Malaysian Mathematical Sciences Society 40:1, pages 1-17.
Crossref
Dongsheng Kang & Jing Yu. (2016) Minimizers to Rayleigh quotients of critical elliptic systems involving different Hardy-type terms. Applied Mathematics Letters 57, pages 97-103.
Crossref
Zhenyu Guo. (2016) Ground States for a Nonlinear Elliptic Equation Involving Multiple Hardy–Sobolev Critical Exponents. Advanced Nonlinear Studies 16:2, pages 333-344.
Crossref
Mohammed Bouchekif & Sofiane Messirdi. (2016) On Nonhomogeneous Elliptic Equations with Critical Sobolev Exponent and Prescribed Singularities. Taiwanese Journal of Mathematics 20:2.
Crossref
Qianqiao Guo & Jarosław Mederski. (2016) Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials. Journal of Differential Equations 260:5, pages 4180-4202.
Crossref
Dongsheng Kang. (2016) Positive minimizers of the best constants and solutions to coupled critical quasilinear systems. Journal of Differential Equations 260:1, pages 133-148.
Crossref
Dongsheng Kang & Jing Yu. (2015) Systems of critical elliptic equations involving Hardy-type terms and large ranges of parameters. Applied Mathematics Letters 46, pages 77-82.
Crossref
Mohammed Bouchekif & Sofiane Messirdi. (2015) On elliptic problems with two critical Hardy–Sobolev exponents at the same pole. Applied Mathematics Letters 42, pages 9-14.
Crossref
Dongsheng KANG, Jing LUO & Xiaolin SHI. (2015) Solutions to elliptic systems involving doubly critical nonlinearities and hardy-type potentials. Acta Mathematica Scientia 35:2, pages 423-438.
Crossref
Dongsheng Kang. (2014) Systems of elliptic equations involving multiple critical nonlinearities and different Hardy-type terms in . Journal of Mathematical Analysis and Applications 420:2, pages 917-929.
Crossref
Dongsheng Kang. (2014) Elliptic systems involving critical nonlinearities and different Hardy-type terms. Journal of Mathematical Analysis and Applications 420:2, pages 930-941.
Crossref
Dongsheng Kang. (2014) Systems of quasilinear elliptic equations involving multiple homogeneous nonlinearities. Applied Mathematics Letters 37, pages 1-6.
Crossref
DongSheng Kang & Fen Yang. (2013) Elliptic systems involving multiple critical nonlinearities and symmetric multi-polar potentials. Science China Mathematics 57:5, pages 1011-1024.
Crossref
Zhao-xia Liu & Zhao-hui Liu. (2013) Existence of solutions for the critical elliptic system with inverse square potentials. Acta Mathematicae Applicatae Sinica, English Series 29:2, pages 315-328.
Crossref
Cristian Cazacu & Enrique Zuazua. 2013. Studies in Phase Space Analysis with Applications to PDEs. Studies in Phase Space Analysis with Applications to PDEs 35 52 .
Cristian Cazacu. (2012) Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results. Journal of Functional Analysis 263:12, pages 3741-3783.
Crossref
Qianqiao Guo, Junqiang Han & Pengcheng Niu. (2012) Existence and multiplicity of solutions for critical elliptic equations with multi-polar potentials in symmetric domains. Nonlinear Analysis: Theory, Methods & Applications 75:15, pages 5765-5786.
Crossref
DongSheng Kang & ShuangJie Peng. (2012) Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials. Science China Mathematics 55:10, pages 2027-2044.
Crossref
Dongsheng Kang. (2018) Asymptotic Properties of Solutions to Semilinear Equations Involving Multiple Critical Exponents. Canadian Mathematical Bulletin 55:3, pages 537-547.
Crossref
Fen Yang & Dongsheng Kang. (2012) Semilinear elliptic systems involving multiple critical exponents and singularities in $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems 32:12, pages 4247-4263.
Crossref
Veronica Felli, Alberto Ferrero & Susanna Terracini. (2012) On the behavior at collisions of solutions to Schrödinger equations with many-particle and cylindrical potentials. Discrete and Continuous Dynamical Systems 32:11, pages 3895-3956.
Crossref
Wang Ying, Luo Dang & Wang Mingxin. (2012) Positive solutions to the p-laplacian with singular weights. Acta Mathematica Scientia 32:3, pages 1002-1020.
Crossref
Monica Musso & Juncheng Wei. (2012) Nonradial Solutions to Critical Elliptic Equations of Caffarelli–Kohn–Nirenberg Type. International Mathematics Research Notices 2012:18, pages 4120-4162.
Crossref
Tsing-San Hsu. (2011) Multiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms. Boundary Value Problems 2011:1.
Crossref
Athanasios N. Lyberopoulos. (2011) Quasilinear scalar field equations with competing potentials. Journal of Differential Equations 251:12, pages 3625-3657.
Crossref
Dongsheng Kang. (2011) Semilinear systems involving multiple critical Hardy–Sobolev exponents and three singular points. Applied Mathematics and Computation 218:8, pages 4514-4522.
Crossref
Tsing-San Hsu. (2011) Multiple positive solutions for semilinear elliptic equations involving multi-singular inverse square potentials and concave–convex nonlinearities. Nonlinear Analysis: Theory, Methods & Applications 74:11, pages 3703-3715.
Crossref
Tsing-San Hsu. (2011) On the Elliptic Problems Involving Multisingular Inverse Square Potentials and Concave-Convex Nonlinearities. Abstract and Applied Analysis 2011, pages 1-22.
Crossref
Li Wang, Qiaoling Wei & Dongsheng Kang. (2011) Multiple positive solutions for -Laplace elliptic equations involving concave–convex nonlinearities and a Hardy-type term. Nonlinear Analysis: Theory, Methods & Applications 74:2, pages 626-638.
Crossref
Yan Huang & Dongsheng Kang. (2011) On the singular elliptic systems involving multiple critical Sobolev exponents. Nonlinear Analysis: Theory, Methods & Applications 74:2, pages 400-412.
Crossref
Dongsheng Kang. (2010) Nontrivial solutions to semilinear elliptic problems involving two critical Hardy–Sobolev exponents. Nonlinear Analysis: Theory, Methods & Applications 72:11, pages 4230-4243.
Crossref
M. Badiale & S. Rolando. (2010) Nonlinear elliptic equations with subhomogeneous potentials. Nonlinear Analysis: Theory, Methods & Applications 72:2, pages 602-617.
Crossref
Yan Huang & Dongsheng Kang. (2009) Elliptic systems involving the critical exponents and potentials. Nonlinear Analysis: Theory, Methods & Applications 71:9, pages 3638-3653.
Crossref
Veronica Felli. (2009) On the existence of ground state solutions to nonlinear Schrödinger equations with multisingular inverse-square anisotropic potentials. Journal d'Analyse Mathématique 108:1, pages 189-217.
Crossref
Dong Sheng Kang. (2009) On the weighted elliptic problems involving multi-singular potentials and multi-critical exponents. Acta Mathematica Sinica, English Series 25:3, pages 435-444.
Crossref
Roberta Filippucci, Patrizia Pucci & Frédéric Robert. (2009) On a p-Laplace equation with multiple critical nonlinearities. Journal de Mathématiques Pures et Appliquées 91:2, pages 156-177.
Crossref
Dongsheng Kang. (2009) Quasilinear elliptic problems involving multiple critical Hardy–Sobolev exponents. Computers & Mathematics with Applications 57:1, pages 107-116.
Crossref
Dongsheng Kang. (2008) On the singular critical quasilinear problems in. Nonlinear Analysis: Theory, Methods & Applications 69:10, pages 3577-3590.
Crossref
DONGSHENG KANG. (2012) ON THE MULTI-SINGULAR ELLIPTIC PROBLEM INVOLVING HARDY–SOBOLEV INEQUALITIES. International Journal of Mathematics 19:07, pages 823-846.
Crossref
Dongsheng Kang. (2008) On the elliptic problems involving multi-singular inverse square potentials and critical Sobolev exponent. Nonlinear Analysis: Theory, Methods & Applications 68:10, pages 3050-3066.
Crossref
Yuping Cao & Dongsheng Kang. (2007) Solutions of a quasilinear elliptic problem involving a critical Sobolev exponent and multiple Hardy-type terms. Journal of Mathematical Analysis and Applications 333:2, pages 889-903.
Crossref
Veronica Felli, Elsa M. Marchini & Susanna Terracini. (2007) On Schrödinger operators with multipolar inverse-square potentials. Journal of Functional Analysis 250:2, pages 265-316.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.