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Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system
Elliptic equations involving linear and superlinear terms and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions
1. | Universidade Federal de São Carlos, Departamento de Matemática, Rod. Washington Luís, Km 235, CEP. 13565-905, São Carlos, SP, Brazil, Brazil |
References:
[1] |
M. Bouchekif and A. Matallah, Singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions,, Electronic Journal of Differential Equations, 2010 (2010), 1.
|
[2] |
H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals,, Proc.Amer. Math. Soc., 88 (1983), 486.
doi: 10.2307/2044999. |
[3] |
H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents,, Comm. Pure Appl. Math., 36 (1983), 437.
doi: 10.1002/cpa.3160360405. |
[4] |
L. Caffarelli, R. Kohn and L. Nirenberg, First order interpolation inequality with weights,, Compos. Math., 53 (1984), 259.
|
[5] |
N. Chaudhuri and M. Ramaswamy, Existence of positive solutions of some semilinear elliptic equations with singular coefficients,, Royal Society of Edinburgh, 131A (2001), 1275.
doi: 10.1017/S0308210500001396. |
[6] |
K. S. Chou and C. W. Chu, On the best constant for a weighted Sobolev-Hardy inequality,, J. London Math. Soc., 2 (1993), 137.
doi: 10.1112/jlms/s2-48.1.137. |
[7] |
L. C. Evans, "Partial Differential Equations,'', Graduate studies in mathematics 19, (1998).
|
[8] |
A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations,, J. Differential Equations, 177 (2001), 494.
doi: 10.1006/jdeq.2000.3999. |
[9] |
P. Han, Quasilinear elliptic problems with critical exponents and Hardy terms,, Nonlinear Anal., 61 (2005), 735.
doi: 10.1016/j.na.2005.01.030. |
[10] |
X. J. Huang, X. P. Wu and C. L. Tang, Multiple positive solutions for semilinear elliptic equations with critical weighted Hardy-Sobolev exponents,, Nonlinear Anal., 74 (2011), 2602.
doi: 10.1016/j.na.2010.12.015. |
[11] |
E. Jannelli, The role played by space dimension in elliptic critical problems,, J. Differential Equations, 156 (1999), 407.
doi: 10.1006/jdeq.1998.3589. |
[12] |
M. Lin, Some further results for a class of weighted nonlinear elliptic equations,, J. Math. Anal. Appl., 337 (2008), 537.
doi: 10.1016/j.jmaa.2007.04.034. |
[13] |
O. H. Miyagaki, On a class of semilinear elliptic problems in $R^N$ with critical growth,, Nonlinear Anal., 29 (1997), 773.
doi: 10.1016/S0362-546X(96)00087-9. |
[14] |
R. S. Rodrigues, On elliptic problems involving critical Hardy-Sobolev exponents and sign-changing function,, Nonlinear Anal., 73 (2010), 857.
doi: 10.1016/j.na.2010.03.053. |
[15] |
M. Struwe, "Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,", Springer-Verlag, (1990).
|
[16] |
B. J. Xuan, S. Su and Y. Yan, Existence results for Brézis-Nirenberg problems with Hardy potential and singular coefficients,, Nonlinear Anal., 67 (2007), 2091.
doi: 10.1016/j.na.2006.09.018. |
[17] |
B. J. Xuan, The solvability of quasilinear Brézis-Nirenberg-type problems with singular weights,, Nonlinear Anal., 62 (2005), 703.
doi: 10.1016/j.na.2005.03.095. |
show all references
References:
[1] |
M. Bouchekif and A. Matallah, Singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions,, Electronic Journal of Differential Equations, 2010 (2010), 1.
|
[2] |
H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals,, Proc.Amer. Math. Soc., 88 (1983), 486.
doi: 10.2307/2044999. |
[3] |
H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents,, Comm. Pure Appl. Math., 36 (1983), 437.
doi: 10.1002/cpa.3160360405. |
[4] |
L. Caffarelli, R. Kohn and L. Nirenberg, First order interpolation inequality with weights,, Compos. Math., 53 (1984), 259.
|
[5] |
N. Chaudhuri and M. Ramaswamy, Existence of positive solutions of some semilinear elliptic equations with singular coefficients,, Royal Society of Edinburgh, 131A (2001), 1275.
doi: 10.1017/S0308210500001396. |
[6] |
K. S. Chou and C. W. Chu, On the best constant for a weighted Sobolev-Hardy inequality,, J. London Math. Soc., 2 (1993), 137.
doi: 10.1112/jlms/s2-48.1.137. |
[7] |
L. C. Evans, "Partial Differential Equations,'', Graduate studies in mathematics 19, (1998).
|
[8] |
A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations,, J. Differential Equations, 177 (2001), 494.
doi: 10.1006/jdeq.2000.3999. |
[9] |
P. Han, Quasilinear elliptic problems with critical exponents and Hardy terms,, Nonlinear Anal., 61 (2005), 735.
doi: 10.1016/j.na.2005.01.030. |
[10] |
X. J. Huang, X. P. Wu and C. L. Tang, Multiple positive solutions for semilinear elliptic equations with critical weighted Hardy-Sobolev exponents,, Nonlinear Anal., 74 (2011), 2602.
doi: 10.1016/j.na.2010.12.015. |
[11] |
E. Jannelli, The role played by space dimension in elliptic critical problems,, J. Differential Equations, 156 (1999), 407.
doi: 10.1006/jdeq.1998.3589. |
[12] |
M. Lin, Some further results for a class of weighted nonlinear elliptic equations,, J. Math. Anal. Appl., 337 (2008), 537.
doi: 10.1016/j.jmaa.2007.04.034. |
[13] |
O. H. Miyagaki, On a class of semilinear elliptic problems in $R^N$ with critical growth,, Nonlinear Anal., 29 (1997), 773.
doi: 10.1016/S0362-546X(96)00087-9. |
[14] |
R. S. Rodrigues, On elliptic problems involving critical Hardy-Sobolev exponents and sign-changing function,, Nonlinear Anal., 73 (2010), 857.
doi: 10.1016/j.na.2010.03.053. |
[15] |
M. Struwe, "Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,", Springer-Verlag, (1990).
|
[16] |
B. J. Xuan, S. Su and Y. Yan, Existence results for Brézis-Nirenberg problems with Hardy potential and singular coefficients,, Nonlinear Anal., 67 (2007), 2091.
doi: 10.1016/j.na.2006.09.018. |
[17] |
B. J. Xuan, The solvability of quasilinear Brézis-Nirenberg-type problems with singular weights,, Nonlinear Anal., 62 (2005), 703.
doi: 10.1016/j.na.2005.03.095. |
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