Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity

Sami Baraket; Makkia Dammak; Taieb Ouni; Frank Pacard

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 6, page 875-895
  • ISSN: 0294-1449

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Baraket, Sami, et al. "Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity." Annales de l'I.H.P. Analyse non linéaire 24.6 (2007): 875-895. <http://eudml.org/doc/78767>.

@article{Baraket2007,
author = {Baraket, Sami, Dammak, Makkia, Ouni, Taieb, Pacard, Frank},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular perturbations; concentration phenomena},
language = {eng},
number = {6},
pages = {875-895},
publisher = {Elsevier},
title = {Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity},
url = {http://eudml.org/doc/78767},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Baraket, Sami
AU - Dammak, Makkia
AU - Ouni, Taieb
AU - Pacard, Frank
TI - Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 6
SP - 875
EP - 895
LA - eng
KW - singular perturbations; concentration phenomena
UR - http://eudml.org/doc/78767
ER -

References

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  1. [1] Baraket S., Pacard F., Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations6 (1998) 1-38. Zbl0890.35047MR1488492
  2. [2] Chang S.Y.A., Yang P., Fourth order equations in conformal geometry, in: Global Analysis and Harmonic Analysis, (Marseille-Luminy, 1999), Smin. Congr., vol. 4, Soc. Math. France, Paris, 2000, pp. 155-165. Zbl0997.35016MR1822359
  3. [3] Chang S.Y.A., Yang P., On a fourth order curvature invariant, in: Branson T. (Ed.), Spectral Problems in Geometry and Arithmetic, Contemporary Mathematics, vol. 237, Amer. Math. Soc., 1999, pp. 9-28. Zbl0982.53035MR1710786
  4. [4] Del Pino M., Kowalczyk M., Musso M., Singular limits in Liouville type equations, Calc. Var. Partial Differential Equations24 (1) (2005) 47-81. Zbl1088.35067MR2157850
  5. [5] Esposito P., Grossi M., Pistoia A., On the existence of blowing-up solutions for a mean field equation, Ann. Inst. H. Poincaré Anal. Non Linéaire22 (2) (2005) 227-257. Zbl1129.35376MR2124164
  6. [6] Lin C.S., Wei J., Locating the peaks of solutions via the maximum principle. II. A local version of the method of moving planes, Comm. Pure Appl. Math.56 (6) (2003) 784-809. Zbl1121.35310MR1959740
  7. [7] Liouville J., Sur l’équation aux différences partielles 2 log λ u v ± λ 2 a 2 = 0 , J. Math.18 (1853) 17-72. 
  8. [8] Lockhart R., McOwen R., Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)12 (3) (1985) 409-447. Zbl0615.58048MR837256
  9. [9] Malchiodi A., Djadli Z., Existence of conformal metrics with constant Q-curvature, Preprint, math.AP/0410141, Ann. of Math., submitted for publication. Zbl1186.53050
  10. [10] Mazzeo R., Elliptic theory of edge operators I, Comm. Partial Differential Equations16 (10) (1991) 1616-1664. Zbl0745.58045MR1133743
  11. [11] Melrose R., The Atiyah–Patodi–Singer Index Theorem, Res. Notes in Math., vol. 4, A.K. Peters Ltd., Wellesley, MA, 1993. Zbl0796.58050
  12. [12] Mignot F., Murat F., Puel J.P., Variation d'un point de retournement par rapport au domaine, Comm. Partial Differential Equations4 (1979) 1263-1297. Zbl0422.35039MR546644
  13. [13] Pacard F., Rivière T., Linear and Nonlinear Aspects of Vortices: The Ginzburg Landau Model, Progress in Nonlinear Differential Equations, vol. 39, Birkhäuser, 2000. Zbl0948.35003MR1763040
  14. [14] Suzuki T., Two-dimensional Emden–Fowler equation with exponential nonlinearity, in: Nonlinear Diffusion Equations and Their Equilibrium States, vol. 3, Birkhäuser, 1992, pp. 493-512. Zbl0792.35061
  15. [15] G. Tarantello, On Chern–Simons Theory, in: H. Berestycki (Ed.), Nonlinear PDE's and Physical Modeling: Superfluidity, Superconductivity and Reactive Flows, Kluver Academic Publishers, in press. Zbl1073.58505
  16. [16] Wente H.C., Counterexample to a conjecture of H. Hopf, Pacific J. Math.121 (1986) 193-243. Zbl0586.53003MR815044
  17. [17] Weston V.H., On the asymptotic solution of a partial differential equation with exponential nonlinearity, SIAM J. Math.9 (1978) 1030-1053. Zbl0402.35038MR512508

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