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Four positive solutions of a quasilinear elliptic equation in $ R^N$
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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).
|
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