-
Previous Article
Four positive solutions of a quasilinear elliptic equation in $ R^N$
- CPAA Home
- This Issue
-
Next Article
Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations
Weighted Sobolev-Hardy spaces and sign-changing solutions of degenerate elliptic equation
1. | Department of Mathematics, South China University of Technology, Guangzhou, 510640, China |
2. | Department of Mathematics, South China University of Technology, Guangzhou 510640 |
References:
[1] |
G. H. Hardy, Note on a theorem of Hilbert,, Mathematische Zeitschrift, 6 (1920), 314.
|
[2] |
H. Brezis and J. L. Vázquez, Blow-up solutions of some nonlinear elliptic problems,, Revista Matem$\acutea$tica de la Universidad Complutense de madrid, 10 (1997), 443.
|
[3] |
F. Gazzola, H. C. Grunau and E. Mitidieri, Hardy inequalities with optimal constants and remainder terms,, Transactions of the American Mathematical Society, 356 (2004), 2149.
|
[4] |
Adimurthi, N. Chaudhuri and M. Ramaswamy, An improved Hardy-Sobolev inequality and its application,, Proceedings of the American Mathematical Society, 130 (2002), 489.
|
[5] |
Adimurthi and M. J. Esteban, An improved Hardy-Sobolev inequality in $W^{1,p}$ and its application to Schrödinger operators,, Nonlinear Differential Equatons and Applications, 12 (2005), 243.
|
[6] |
B. Abdellaoui, E. Colorado and I. Peral, Some improved Caffarelli-Kohn-Nirenberg inequalities,, Calculus of Variations and Partial Differential Equations, 23 (2005), 327.
|
[7] |
Y. T. Shen, The Dirichlet problem for degenerate or singular elliptic equation of high order,, Journal of China University of Science and Technology, 10 (1980), 1. Google Scholar |
[8] |
Y. T. Shen and X. K. Guo, Weighted Poincaré inequalities on unbounded domains and nonlinear elliptic boundary value problems,, Acta Mathematica Scientia, 4 (1984), 277.
|
[9] |
G. Barbatis, S. Filippas and A. Tertikas, A unified approach to improved $L^p$ Hardy inequalities with best constants,, Trans. Amer. Math. Soc., 356 (2004), 2169. Google Scholar |
[10] |
H. Brezis and M. Marcus, Hardy's inequalities revisited,, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, 25 (1997), 217.
|
[11] |
S. Filippas, V. G. Maz'ya and A. Tertikas, On a question of Brezis and marcus,, Calc. of Variations and P.D.E., 25 (2006), 491.
|
[12] |
S. Filippas, V. G. Maz'ya and A. Tertikas, Critical Hardy-Sobolev Inequalities,, Journal de Math$\acutee$matiques Pures et Appliqu$\acutee$es, 87 (2007), 37.
|
[13] |
J. Dávila and L. Dupaigne, Hardy-type inequalities,, J. Eur. Math. Soc., 6 (2004), 335.
|
[14] |
M. K. V. Murthy and G. Stampacchia, Boundary value problems for some degenerate elliptic operators,, Annali Mat. Pura Appl., 80 (1968), 1.
|
[15] |
A. Kristály and C. Varga, Multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity,, J. Math. Anal. Appl., 352 (2009), 139.
|
[16] |
Y. M. Chen, Regularity of solutions to the Dirichlet problem for degenerate elliptic equation,, Chin. Ann. Math., 24 (2003), 529.
|
[17] |
Y. T. Shen and Y. X. Yao, Nonlinear elliptic equations with critical potential and critical parameter,, Proceedings of the Royal Society of Edinburgh, 136 (2006), 1041.
|
[18] |
M. M. Zou, "Sign-Changing Critical Point Theory,", Springer-Verlag, (2008). Google Scholar |
[19] |
E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities,, Courant Lecture Notes in Mathematics, 5 (1999).
|
show all references
References:
[1] |
G. H. Hardy, Note on a theorem of Hilbert,, Mathematische Zeitschrift, 6 (1920), 314.
|
[2] |
H. Brezis and J. L. Vázquez, Blow-up solutions of some nonlinear elliptic problems,, Revista Matem$\acutea$tica de la Universidad Complutense de madrid, 10 (1997), 443.
|
[3] |
F. Gazzola, H. C. Grunau and E. Mitidieri, Hardy inequalities with optimal constants and remainder terms,, Transactions of the American Mathematical Society, 356 (2004), 2149.
|
[4] |
Adimurthi, N. Chaudhuri and M. Ramaswamy, An improved Hardy-Sobolev inequality and its application,, Proceedings of the American Mathematical Society, 130 (2002), 489.
|
[5] |
Adimurthi and M. J. Esteban, An improved Hardy-Sobolev inequality in $W^{1,p}$ and its application to Schrödinger operators,, Nonlinear Differential Equatons and Applications, 12 (2005), 243.
|
[6] |
B. Abdellaoui, E. Colorado and I. Peral, Some improved Caffarelli-Kohn-Nirenberg inequalities,, Calculus of Variations and Partial Differential Equations, 23 (2005), 327.
|
[7] |
Y. T. Shen, The Dirichlet problem for degenerate or singular elliptic equation of high order,, Journal of China University of Science and Technology, 10 (1980), 1. Google Scholar |
[8] |
Y. T. Shen and X. K. Guo, Weighted Poincaré inequalities on unbounded domains and nonlinear elliptic boundary value problems,, Acta Mathematica Scientia, 4 (1984), 277.
|
[9] |
G. Barbatis, S. Filippas and A. Tertikas, A unified approach to improved $L^p$ Hardy inequalities with best constants,, Trans. Amer. Math. Soc., 356 (2004), 2169. Google Scholar |
[10] |
H. Brezis and M. Marcus, Hardy's inequalities revisited,, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, 25 (1997), 217.
|
[11] |
S. Filippas, V. G. Maz'ya and A. Tertikas, On a question of Brezis and marcus,, Calc. of Variations and P.D.E., 25 (2006), 491.
|
[12] |
S. Filippas, V. G. Maz'ya and A. Tertikas, Critical Hardy-Sobolev Inequalities,, Journal de Math$\acutee$matiques Pures et Appliqu$\acutee$es, 87 (2007), 37.
|
[13] |
J. Dávila and L. Dupaigne, Hardy-type inequalities,, J. Eur. Math. Soc., 6 (2004), 335.
|
[14] |
M. K. V. Murthy and G. Stampacchia, Boundary value problems for some degenerate elliptic operators,, Annali Mat. Pura Appl., 80 (1968), 1.
|
[15] |
A. Kristály and C. Varga, Multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity,, J. Math. Anal. Appl., 352 (2009), 139.
|
[16] |
Y. M. Chen, Regularity of solutions to the Dirichlet problem for degenerate elliptic equation,, Chin. Ann. Math., 24 (2003), 529.
|
[17] |
Y. T. Shen and Y. X. Yao, Nonlinear elliptic equations with critical potential and critical parameter,, Proceedings of the Royal Society of Edinburgh, 136 (2006), 1041.
|
[18] |
M. M. Zou, "Sign-Changing Critical Point Theory,", Springer-Verlag, (2008). Google Scholar |
[19] |
E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities,, Courant Lecture Notes in Mathematics, 5 (1999).
|
[1] |
Yanfang Peng, Jing Yang. Sign-changing solutions to elliptic problems with two critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2015, 14 (2) : 439-455. doi: 10.3934/cpaa.2015.14.439 |
[2] |
Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037 |
[3] |
Tsung-Fang Wu. On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function. Communications on Pure & Applied Analysis, 2008, 7 (2) : 383-405. doi: 10.3934/cpaa.2008.7.383 |
[4] |
Jing Zhang, Shiwang Ma. Positive solutions of perturbed elliptic problems involving Hardy potential and critical Sobolev exponent. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1999-2009. doi: 10.3934/dcdsb.2016033 |
[5] |
Salomón Alarcón, Jinggang Tan. Sign-changing solutions for some nonhomogeneous nonlocal critical elliptic problems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 5825-5846. doi: 10.3934/dcds.2019256 |
[6] |
Fengshuang Gao, Yuxia Guo. Multiple solutions for a critical quasilinear equation with Hardy potential. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1977-2003. doi: 10.3934/dcdss.2019128 |
[7] |
Zhengping Wang, Huan-Song Zhou. Radial sign-changing solution for fractional Schrödinger equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 499-508. doi: 10.3934/dcds.2016.36.499 |
[8] |
Xiaomei Sun, Wenyi Chen. Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent. Communications on Pure & Applied Analysis, 2011, 10 (2) : 527-540. doi: 10.3934/cpaa.2011.10.527 |
[9] |
Jinhui Chen, Haitao Yang. A result on Hardy-Sobolev critical elliptic equations with boundary singularities. Communications on Pure & Applied Analysis, 2007, 6 (1) : 191-201. doi: 10.3934/cpaa.2007.6.191 |
[10] |
Craig Cowan. Optimal Hardy inequalities for general elliptic operators with improvements. Communications on Pure & Applied Analysis, 2010, 9 (1) : 109-140. doi: 10.3934/cpaa.2010.9.109 |
[11] |
Chunhua Wang, Jing Yang. Infinitely many solutions for an elliptic problem with double critical Hardy-Sobolev-Maz'ya terms. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1603-1628. doi: 10.3934/dcds.2016.36.1603 |
[12] |
Boumediene Abdellaoui, Ahmed Attar. Quasilinear elliptic problem with Hardy potential and singular term. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1363-1380. doi: 10.3934/cpaa.2013.12.1363 |
[13] |
Mateus Balbino Guimarães, Rodrigo da Silva Rodrigues. Elliptic equations involving linear and superlinear terms and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2697-2713. doi: 10.3934/cpaa.2013.12.2697 |
[14] |
Yohei Sato, Zhi-Qiang Wang. On the least energy sign-changing solutions for a nonlinear elliptic system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2151-2164. doi: 10.3934/dcds.2015.35.2151 |
[15] |
Aixia Qian, Shujie Li. Multiple sign-changing solutions of an elliptic eigenvalue problem. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 737-746. doi: 10.3934/dcds.2005.12.737 |
[16] |
Jann-Long Chern, Yong-Li Tang, Chuan-Jen Chyan, Yi-Jung Chen. On the uniqueness of singular solutions for a Hardy-Sobolev equation. Conference Publications, 2013, 2013 (special) : 123-128. doi: 10.3934/proc.2013.2013.123 |
[17] |
Gui-Dong Li, Chun-Lei Tang. Existence of ground state solutions for Choquard equation involving the general upper critical Hardy-Littlewood-Sobolev nonlinear term. Communications on Pure & Applied Analysis, 2019, 18 (1) : 285-300. doi: 10.3934/cpaa.2019015 |
[18] |
Guirong Liu, Yuanwei Qi. Sign-changing solutions of a quasilinear heat equation with a source term. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1389-1414. doi: 10.3934/dcdsb.2013.18.1389 |
[19] |
Wenxiong Chen, Chao Jin, Congming Li, Jisun Lim. Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations. Conference Publications, 2005, 2005 (Special) : 164-172. doi: 10.3934/proc.2005.2005.164 |
[20] |
Stathis Filippas, Luisa Moschini, Achilles Tertikas. Trace Hardy--Sobolev--Maz'ya inequalities for the half fractional Laplacian. Communications on Pure & Applied Analysis, 2015, 14 (2) : 373-382. doi: 10.3934/cpaa.2015.14.373 |
2018 Impact Factor: 0.925
Tools
Metrics
Other articles
by authors
[Back to Top]