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Supercritical problems in domains with thin toroidal holes
1. | Departamento de Matemática, Pontificia Universidad Catóica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile |
2. | Dipartimento SBAI, Università di Roma "La Sapienza", via Antonio Scarpa 16, 00161 Roma |
References:
[1] |
N. Ackermann, M. Clápp and A. Pistoia, Boundary clustered layers near the higher critical exponents, J. Differential Equations, 254 (2013), 4168-4193.
doi: 10.1016/j.jde.2013.02.015. |
[2] |
A. Bahri and J. M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., 41 (1988), 253-294.
doi: 10.1002/cpa.3160410302. |
[3] |
A. Bahri, Y.-Y. Li and O. Rey, On a variational problem with lack of compactness: The topological effect of the critical points at infinity, Calc. Var. Partial Diff. Eq., 3 (1995), 67-93.
doi: 10.1007/BF01190892. |
[4] |
T. Bartsch, A. M. Micheletti and A. Pistoia, On the existence and the profile of nodal solutions of elliptic equations involving critical growth, Calc. Var. Partial Diff. Eq., 26 (2006), 265-282.
doi: 10.1007/s00526-006-0004-6. |
[5] |
M. Clapp, J. Faya and A. Pistoia, Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents, Calc. Var. Partial Diff. Eq., 48 (2013), 611-623.
doi: 10.1007/s00526-012-0564-6. |
[6] |
M. Clapp, J. Faya and A. Pistoia, Positive solutions to a supercritical elliptic problem which concentrate along a think spherical hole, J. Anal. Math., in press. |
[7] |
J. M. Coron, Topologie et cas limite des injections de sobolev, C. R. Acad. Sci. Paris Ser. I Math., 299 (1984), 209-212. |
[8] |
M. del Pino, P. Felmer and M. Musso, Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. Partial Diff. Eq., 16 (2003), 113-145.
doi: 10.1007/s005260100142. |
[9] |
M. del Pino, M. Musso and F. Pacard, Bubbling along boundary geodesics near the second critical exponent, J. Eur. Math. Soc., 12 (2010), 1553-1605.
doi: 10.4171/JEMS/241. |
[10] |
M. del Pino and J. Wei, Supercritical elliptic problems in domains with small holes, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 507-520.
doi: 10.1016/j.anihpc.2006.03.001. |
[11] |
E. N. Dancer and J. Wei, Sign-changing solutions for supercritical elliptic problems in domains with small holes, Manuscripta Math, 123 (2007), 493-511.
doi: 10.1007/s00229-007-0110-6. |
[12] |
Y. Ge, M. Musso and A. Pistoia, Sign changing tower of bubbles for an elliptic problem at the critical exponent in pierced non-symmetric domains, Commun. Partial Differ. Equ., 35 (2010), 1419-1457.
doi: 10.1080/03605302.2010.490286. |
[13] |
S. Kim and A. Pistoia, Boundary towers of layers for some supercritical problems, J. Differential Equations, 255 (2013), 2302-2339.
doi: 10.1016/j.jde.2013.06.017. |
[14] |
S. Kim and A. Pistoia, Clustered boundary layer sign changing solutions for a supercritical problem, J. London Math. Soc., 88 (2013), 227-250.
doi: 10.1112/jlms/jdt006. |
[15] |
J. Kazdan and F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., 28 (1975), 567-597.
doi: 10.1002/cpa.3160280502. |
[16] |
M. Musso and A. Pistoia, Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains, J. Math. Pures Appl., 86 (2006), 510-528.
doi: 10.1016/j.matpur.2006.10.006. |
[17] |
M. Musso and A. Pistoia, Tower of bubbles for almost critical problems in general domains, J. Math. Pures Appl., 93 (2010), 1-40.
doi: 10.1016/j.matpur.2009.08.001. |
[18] |
D. Passaseo, Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Func. Anal., 114 (1993), 97-105.
doi: 10.1006/jfan.1993.1064. |
[19] |
D. Passaseo, New nonexistence results for elliptic equations with supercritical nonlinearity, Diff. Int. Equat., 8 (1995), 577-586. |
[20] |
S. I. Pohožaev, Eigenfunctions of the equation $\Delta u + \lambda f(u) = 0$, Dokl. Akad. Nauk SSSR, 165 (1965), 36-39. |
[21] |
A. Pistoia and T. Weth, Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 325-340.
doi: 10.1016/j.anihpc.2006.03.002. |
[22] |
S. Yan and J. Wei, Infinitely many positive solutions for an elliptic problem with critical or supercritical growth, J. Math Pures Appl., 96 (2011), 307-333.
doi: 10.1016/j.matpur.2011.01.006. |
show all references
References:
[1] |
N. Ackermann, M. Clápp and A. Pistoia, Boundary clustered layers near the higher critical exponents, J. Differential Equations, 254 (2013), 4168-4193.
doi: 10.1016/j.jde.2013.02.015. |
[2] |
A. Bahri and J. M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., 41 (1988), 253-294.
doi: 10.1002/cpa.3160410302. |
[3] |
A. Bahri, Y.-Y. Li and O. Rey, On a variational problem with lack of compactness: The topological effect of the critical points at infinity, Calc. Var. Partial Diff. Eq., 3 (1995), 67-93.
doi: 10.1007/BF01190892. |
[4] |
T. Bartsch, A. M. Micheletti and A. Pistoia, On the existence and the profile of nodal solutions of elliptic equations involving critical growth, Calc. Var. Partial Diff. Eq., 26 (2006), 265-282.
doi: 10.1007/s00526-006-0004-6. |
[5] |
M. Clapp, J. Faya and A. Pistoia, Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents, Calc. Var. Partial Diff. Eq., 48 (2013), 611-623.
doi: 10.1007/s00526-012-0564-6. |
[6] |
M. Clapp, J. Faya and A. Pistoia, Positive solutions to a supercritical elliptic problem which concentrate along a think spherical hole, J. Anal. Math., in press. |
[7] |
J. M. Coron, Topologie et cas limite des injections de sobolev, C. R. Acad. Sci. Paris Ser. I Math., 299 (1984), 209-212. |
[8] |
M. del Pino, P. Felmer and M. Musso, Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. Partial Diff. Eq., 16 (2003), 113-145.
doi: 10.1007/s005260100142. |
[9] |
M. del Pino, M. Musso and F. Pacard, Bubbling along boundary geodesics near the second critical exponent, J. Eur. Math. Soc., 12 (2010), 1553-1605.
doi: 10.4171/JEMS/241. |
[10] |
M. del Pino and J. Wei, Supercritical elliptic problems in domains with small holes, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 507-520.
doi: 10.1016/j.anihpc.2006.03.001. |
[11] |
E. N. Dancer and J. Wei, Sign-changing solutions for supercritical elliptic problems in domains with small holes, Manuscripta Math, 123 (2007), 493-511.
doi: 10.1007/s00229-007-0110-6. |
[12] |
Y. Ge, M. Musso and A. Pistoia, Sign changing tower of bubbles for an elliptic problem at the critical exponent in pierced non-symmetric domains, Commun. Partial Differ. Equ., 35 (2010), 1419-1457.
doi: 10.1080/03605302.2010.490286. |
[13] |
S. Kim and A. Pistoia, Boundary towers of layers for some supercritical problems, J. Differential Equations, 255 (2013), 2302-2339.
doi: 10.1016/j.jde.2013.06.017. |
[14] |
S. Kim and A. Pistoia, Clustered boundary layer sign changing solutions for a supercritical problem, J. London Math. Soc., 88 (2013), 227-250.
doi: 10.1112/jlms/jdt006. |
[15] |
J. Kazdan and F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., 28 (1975), 567-597.
doi: 10.1002/cpa.3160280502. |
[16] |
M. Musso and A. Pistoia, Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains, J. Math. Pures Appl., 86 (2006), 510-528.
doi: 10.1016/j.matpur.2006.10.006. |
[17] |
M. Musso and A. Pistoia, Tower of bubbles for almost critical problems in general domains, J. Math. Pures Appl., 93 (2010), 1-40.
doi: 10.1016/j.matpur.2009.08.001. |
[18] |
D. Passaseo, Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Func. Anal., 114 (1993), 97-105.
doi: 10.1006/jfan.1993.1064. |
[19] |
D. Passaseo, New nonexistence results for elliptic equations with supercritical nonlinearity, Diff. Int. Equat., 8 (1995), 577-586. |
[20] |
S. I. Pohožaev, Eigenfunctions of the equation $\Delta u + \lambda f(u) = 0$, Dokl. Akad. Nauk SSSR, 165 (1965), 36-39. |
[21] |
A. Pistoia and T. Weth, Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 325-340.
doi: 10.1016/j.anihpc.2006.03.002. |
[22] |
S. Yan and J. Wei, Infinitely many positive solutions for an elliptic problem with critical or supercritical growth, J. Math Pures Appl., 96 (2011), 307-333.
doi: 10.1016/j.matpur.2011.01.006. |
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