Concentrating solutions for the Hénon equation in ℝ2

Journal d'Analyse Mathematique

Volumn 100, Issue , 2006, Pages 249-280

  Esposito, Pierpaolo ^a,b   Pistoia, Angela ^c   Wei, Juncheng ^d  

^a ROMA TRE UNIVERSITY   (Italy)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

^d CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247498143     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02916763     Document Type: Article

References (24)

1. Adimurthi and M. Grossi, Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity, Proc. Amer. Math. Soc. 132 (2004), 1013-1019.
2. S. Baraket and F. Pacard, Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations 6 (1998), 1-38.
3. J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states, preprint (2002).
4. J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states, II., J. Differential Equations 216 (2005), 78-108.
5. D. Cao and S. Peng, The asymptotic behavior of the ground state solutions for Hénon equation, J. Math. Anal. Appl., 278 (2003), 1-17.
6. D. Chae and O. Imanuvilov, The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000), 119-142.
7. W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615-623.
8. G. Chen, W.-M. Ni and J. Zhou, Algorithms and visualization for solutions of nonlinear elliptic equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 10 (2000), 1565-1612.
9. M. del Pino, M. Kowalczyk and M. Musso, Singular limits in Liouville-type equations, Calc. Var. Partial Differential Equations 24 (2005), 47-81.
10. K. El Mehdi and M. Grossi, Asymptotic estimates and qualitative properties of an elliptic problem in dimension two, Adv. Nonlinear Stud. 4 (2004), 15-36.
11. P. Esposito, Blow up solutions for a Liouville equation with singular data, SIAM J. Math. Anal. 36 (2005), 1310-1345.
12. P. Esposito, Blow up solutions for a Liouville equation with singular data, in Recent Advances in Elliptic and Parabolic Problems, eds. Chiun-Chuan Chen, Michel Chipot and Chang-Shou Lin, World Sci. Publ., Hackensack, NJ, 2005, pp. 61-79.
13. P. Esposito, M. Grossi and A. Pistoia, On the existence of blowing-up solutions for a mean field equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 22(2005), 227-257.
14. P. Esposito, M. Musso and A. Pistoia, Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent, J. Differential Equations, 227 (2006), 29-68.
15. P. Esposito, M. Musso and A. Pistoia, On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity, Proc. London Math. Soc., to appear.
16. M. Hénon, Numerical experiments on the stability of spherical stellar systems, Astronomy and Astrophysics 24 (1973), 229-238.
17. L. Ma and J. Wei, Convergence for a Liouville equation, Comment. Math. Helv. 76 (2001), 506-514.
18. W.-M. Ni, A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J. 6 (1982), 801-807.
19. S. Peng, Multiple boundary concentrating solutions to Dirichlet problem of Hénon equation, Acta Math. Appl. Sin. Engle. Ser. 22 (2006), 137-162.
20. A. Pistoia and E. Serra, Multi-peak solutions for the Hénon equation with slightly subcritical growth, Math. Z., to appear.
21. N : symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), 967-985.
22. X. Ren and J. Wei, On a two-dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc. 343 (1994), 749-763.
23. X. Ren and J. Wei, Single point condensation and least energy solutions, Proc. Amer. Math. Soc. 124 (1996), 111-120.
24. D. Smets, J. Su and M. Willem, Non-radial ground states for the Hénon equation, Commun. Contemp. Math. 4 (2002), 467-480.