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Positive solutions of perturbed elliptic problems involving Hardy potential and critical Sobolev exponent
1. | Mathematics Science College, Inner Mongolia Normal University, Hohhot 010022, China |
2. | School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 |
References:
[1] |
A. Ambrosetti and Andrea Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on $\mathbb{R}^N2$, Birkhäuser Verlag, 2006. |
[2] |
A. Ambrosetti, J. Garcia Azorero and I. Peral, Perturbation of $\Delta u+u^{\frac{N+2}{N-2}}=0$, The scalar curvature problems in $\mathbb{R}^N2$ and related topics, J. Funct. Anal, 165 (1999), 117-149.
doi: 10.1006/jfan.1999.3390. |
[3] |
A. Ambrosetti and M. Badiale, Variational perturbative methods and bifurcation of bounds states from the the essential spectrum, Proc. Roy. Soc. Edinburgh A, 128 (1998), 1131-1161.
doi: 10.1017/S0308210500027268. |
[4] |
A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of nonlinear Schrödinger equations, Arch. Rational Mech. Anal., 140 (1997), 285-300.
doi: 10.1007/s002050050067. |
[5] |
M. Badiale, J. Garcia Azorero and I. Peral, Perturbation results for an anisotropic SchrHodinger equation via a variational form, NoDEA, 7 (2000), 201-230.
doi: 10.1007/s000300050005. |
[6] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations I - existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.
doi: 10.1007/BF00250555. |
[7] |
K. J. Brown and N. Stavrakakis, Global bifurcation results for a semilinear elliptic equation on all $\mathbb{R}^N2$, Duke Math. J., 85 (1996), 77-94.
doi: 10.1215/S0012-7094-96-08503-8. |
[8] |
F. Catrina and Z. Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extermal functions, Comm. Pure Appl. Math., 54 (2001), 229-258.
doi: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I. |
[9] |
S. Cingolani, Positive solutions to perturbed elliptic problems in $\mathbb{R}^N2$ involving critical Sobolev exponent, Nonlinear Analysis, 48 (2002), 1165-1178.
doi: 10.1016/S0362-546X(00)00245-5. |
[10] |
O. Rey, The role of the Green's function in a non-linear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal., 89 (1990), 1-52.
doi: 10.1016/0022-1236(90)90002-3. |
[11] |
N. S. Trudinger, On Harnack type inequalities and theri application to quasilinear elliptic equations, Comm. Pure Appl. Math., 20 (1967), 721-747.
doi: 10.1002/cpa.3160200406. |
show all references
References:
[1] |
A. Ambrosetti and Andrea Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on $\mathbb{R}^N2$, Birkhäuser Verlag, 2006. |
[2] |
A. Ambrosetti, J. Garcia Azorero and I. Peral, Perturbation of $\Delta u+u^{\frac{N+2}{N-2}}=0$, The scalar curvature problems in $\mathbb{R}^N2$ and related topics, J. Funct. Anal, 165 (1999), 117-149.
doi: 10.1006/jfan.1999.3390. |
[3] |
A. Ambrosetti and M. Badiale, Variational perturbative methods and bifurcation of bounds states from the the essential spectrum, Proc. Roy. Soc. Edinburgh A, 128 (1998), 1131-1161.
doi: 10.1017/S0308210500027268. |
[4] |
A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of nonlinear Schrödinger equations, Arch. Rational Mech. Anal., 140 (1997), 285-300.
doi: 10.1007/s002050050067. |
[5] |
M. Badiale, J. Garcia Azorero and I. Peral, Perturbation results for an anisotropic SchrHodinger equation via a variational form, NoDEA, 7 (2000), 201-230.
doi: 10.1007/s000300050005. |
[6] |
H. Berestycki and P. L. Lions, Nonlinear scalar field equations I - existence of a ground state, Arch. Rational Mech. Anal., 82 (1983), 313-345.
doi: 10.1007/BF00250555. |
[7] |
K. J. Brown and N. Stavrakakis, Global bifurcation results for a semilinear elliptic equation on all $\mathbb{R}^N2$, Duke Math. J., 85 (1996), 77-94.
doi: 10.1215/S0012-7094-96-08503-8. |
[8] |
F. Catrina and Z. Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extermal functions, Comm. Pure Appl. Math., 54 (2001), 229-258.
doi: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I. |
[9] |
S. Cingolani, Positive solutions to perturbed elliptic problems in $\mathbb{R}^N2$ involving critical Sobolev exponent, Nonlinear Analysis, 48 (2002), 1165-1178.
doi: 10.1016/S0362-546X(00)00245-5. |
[10] |
O. Rey, The role of the Green's function in a non-linear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal., 89 (1990), 1-52.
doi: 10.1016/0022-1236(90)90002-3. |
[11] |
N. S. Trudinger, On Harnack type inequalities and theri application to quasilinear elliptic equations, Comm. Pure Appl. Math., 20 (1967), 721-747.
doi: 10.1002/cpa.3160200406. |
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