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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 4
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Articles

Bubble tower phenomena for an almost critical Hénon type problem

Pages 636-657 | Received 15 Dec 2016, Accepted 01 Jul 2018, Published online: 09 Aug 2018

References

  • Hénon M. Numerical experiments on the stability of spherical stellar systems. Astron Astrophys. 1973;24:229–238.
  • Ni W-M. A nonlinear Dirichlet problem on the unit ball and its applications. Indiana Univ Math J. 1982;31(6):801–807. doi: 10.1512/iumj.1982.31.31056
  • Smets D, Su J, Willem M. Nonradial ground states for the Hénon equation. Comm Contemp Math. 2002;4:467–480. doi: 10.1142/S0219199702000725
  • Cao D, Peng S. The asymptotic behavior of the ground state solutions for Hénon equation. J Math Anal Appl. 2003;278:1–17. doi: 10.1016/S0022-247X(02)00292-5
  • Pistoia A, Serra E. Multi-peak solutions for the Hénon equation with slightly subcritical growth. Math Z. 2007;256:75–97. doi: 10.1007/s00209-006-0060-9
  • Peng S. Multiple boundary concentrating solutions to Dirichlet problem of Hénon equation. Acta Math Appl Sin. 2006;22:137–162. doi: 10.1007/s10255-005-0293-0
  • Wei J, Yan S. Infinitely many non-radial solutions for the Hénon equation with critical growth. Rev Mat Iberoam. 2013;29:997–1020. doi: 10.4171/RMI/747
  • Byeon J, Wang Z-Q. On the Hénon equation: asymptotic profile of ground states. I. Ann Inst H Poincare Anal Non Linaire Anal. 2006;23:803–828. doi: 10.1016/j.anihpc.2006.04.001
  • Byeon J, Wang Z-Q. On the Hénon equation: asymptotic profile of ground states. II. J Differ Equ. 2005;216:78–108. doi: 10.1016/j.jde.2005.02.018
  • Cao D, Peng S, Yan S. Asymptotic behavior of the ground state solutions for Hénon equation. IMA J Appl Math. 2009;74:468–480. doi: 10.1093/imamat/hxn035
  • Hirano N. Existence of positive solutions for the Hénon equation involving critical Sobolev exponent. J Differ Equ. 2009;247:1311–1333. doi: 10.1016/j.jde.2009.06.008
  • Serra E. Non-radial positive solutions for the Hénon equation with critical growth. Calc Var Partial Differ Equ. 2005;23:301–326. doi: 10.1007/s00526-004-0302-9
  • Pohozaev S. Eigenfunctions of the equation Δu+λf(u)=0. Soviet Math Dokl. 1965;6:1408–1411.
  • Gladiali F, Grossi M. Supercritical elliptic problem with nonautonomous nonlinearities. J Differ Equ. 2012;253:2616–2645. doi: 10.1016/j.jde.2012.07.006
  • Liu Z, Peng S. Solutions with large number of peaks for the supercritical Hénon equation. Pacific J Math. 2016;280:115–139. doi: 10.2140/pjm.2016.280.115
  • Cao D, Liu Z, Peng S. Sign-changing bubble tower solutions for the supercritical Hénon equations. Annali di Matematica. 2018;197:1227–1246.
  • Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm Pure Appl Math. 1983;36:437–477. doi: 10.1002/cpa.3160360405
  • Del Pino M, Dolbeault J, Musso M. “Bubble-tower” radial solutions in the slightly supercritical Brezis-Nirenberg problem. J Differ Equ. 2003;193:280–306. doi: 10.1016/S0022-0396(03)00151-7
  • Del Pino M, Dolbeault J, Musso M. The Brezis-Nirenberg problem near criticality in dimension 3. J Math Pures Appl. 2004;83:1405–1456. doi: 10.1016/j.matpur.2004.02.007
  • Ge Y, Jing R, Pacard F. Bubble towers for supercritical semilinear elliptic equations. J Funct Anal. 2005;221:251–302. doi: 10.1016/j.jfa.2004.09.011
  • Musso M, Pistoia A. Multispike solutions for a nonlinear elliptic problem involving the critical Sobolev exponent. Indiana Univ Math J. 2002;51(3):541–579. doi: 10.1512/iumj.2002.51.2199
  • Musso M, Pistoia A. Double blow-up solutions for a Brezis-Nirenberg type problem. Commun Contemp Math. 2003;5(5):775–802. doi: 10.1142/S0219199703001099
  • Rey O. The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent. J Funct Anal. 1990;89(1):1–52. doi: 10.1016/0022-1236(90)90002-3
  • Gladiali F, Grossi M. Linear perturbations for the critical Hénon problem. Differ Integral Equ. 2015;28(7–8): 733–752.
  • Cao D, Peng S. Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth. Ann Mat Pura Appl. 2006;185:189–205. doi: 10.1007/s10231-005-0150-z
  • Han P. Asymptotic behavior of solutions to semilinear elliptic equations with Hardy potential. Proc Amer Math Soc. 2007;135:365–372. doi: 10.1090/S0002-9939-06-08462-0
  • Smets D. Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans Amer Math Soc. 2005;357:2909–2938. doi: 10.1090/S0002-9947-04-03769-9
  • Terracini S. On the positive entire solutions to a class of equations with singular coefficients and critical exponents. Adv Differ Equ. 1996;1:241–264.
  • Gladiali F, Grossi M, Neves SLN. Nonradial solutions for the Hénon equation in RN. Adv Math. 2013;249:1–36. doi: 10.1016/j.aim.2013.07.022
  • Pistoia A, Weth T. Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem. Ann Inst H Poincaré Anal Non Linéaire. 2007;24:325–340. doi: 10.1016/j.anihpc.2006.03.002
  • Contreras A, Del Pino M. Nodal bubble-tower solutions to radial elliptic problems near criticality. Discrete Contin Dyn Syst. 2006;16:525–539. doi: 10.3934/dcds.2006.16.525
  • Liu Z. Nodal bubble-tower solutions for a semilinear elliptic problem with competing powers. Discrete Contin Dyn Syst. 2017;37(10):5299–5317. doi: 10.3934/dcds.2017230

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