Blow-up and nonexistence of sign changing solutions to the Brezis-Nirenberg problem in dimension three
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 4, pp. 567-589.
DOI : 10.1016/j.anihpc.2005.07.001
Ben Ayed, Mohamed  ; El Mehdi, Khalil 1 ; Pacella, Filomena 

1 Université de Nouakchott Faculté des Sciences et Techniques BP 5026, Nouakchott MAURITANIA
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     title = {Blow-up and nonexistence of sign changing solutions to the {Brezis-Nirenberg} problem in dimension three},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {567--589},
     publisher = {Elsevier},
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Ben Ayed, Mohamed; El Mehdi, Khalil; Pacella, Filomena. Blow-up and nonexistence of sign changing solutions to the Brezis-Nirenberg problem in dimension three. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 4, pp. 567-589. doi : 10.1016/j.anihpc.2005.07.001. http://www.numdam.org/articles/10.1016/j.anihpc.2005.07.001/

[1] Adimurthi , Yadava S.L., An elementary proof of the uniqueness of positive radial solutions of a quasilinear Dirichlet problem, Arch. Rational Mech. Anal. 127 (1994) 219-229. | MR | Zbl

[2] Atkinson F.V., Brezis H., Peletier L.A., Solutions d'équations elliptiques avec exposant de Sobolev critique qui changent de signe, C. R. Acad. Sci. Paris, Sér. I 306 (1988) 711-714. | MR | Zbl

[3] Atkinson F.V., Brezis H., Peletier L.A., Nodal solutions of elliptic equations with critical Sobolev exponents, J. Differential Equations 85 (1990) 151-170. | MR | Zbl

[4] Bahri A., Critical Points at Infinity in Some Variational Problems, Pitman Res. Notes Math. Ser., vol. 182, Longman Sci. Tech., Harlow, 1989. | MR | Zbl

[5] Ben Ayed M., El Mehdi K., Hammami M., A nonexistence result for Yamabe type problems on thin annuli, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002) 715-744. | Numdam | MR | Zbl

[6] Brezis H., Some variational problems with lack of compactness, Proc. Sympos. Pure Math. 45 (1986) 165-201. | MR | Zbl

[7] Brezis H., Kato T., Remarks on the Schroedinger operator with singular complex potential, J. Math. Pures Appl. 58 (1979) 137-151. | MR | Zbl

[8] Brezis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983) 437-477. | MR | Zbl

[9] Caffarelli L., Gidas B., Spruck J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR | Zbl

[10] Clapp M., Weth T., Multiple solutions for the Brezis-Nirenberg problem, Adv. Differential Equations 10 (2005) 463-480. | MR | Zbl

[11] Druet O., Elliptic equations with critical Sobolev exponent in dimension 3, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002) 125-142. | Numdam | MR | Zbl

[12] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, Springer-Verlag, Berlin, 1977. | MR | Zbl

[13] Li Y.Y., Prescribing scalar curvature on S n and related topics, Part I, J. Differential Equations 120 (1995) 319-410. | MR | Zbl

[14] Rey O., The role of the Green's function in a nonlinear elliptic equation involving critical Sobolev exponent, J. Funct. Anal. 89 (1990) 1-52. | MR | Zbl

[15] Schoen R., Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, in: Topics in Calculus of Variations, Montecatini Terme, 1987, Lectures Notes in Math., vol. 1365, Springer-Verlag, Berlin, 1989, pp. 120-154. | MR | Zbl

[16] Schoen R., On the number of solutions of constant scalar curvature in a conformal class, in: Lawson H.B., Tenenblat K. (Eds.), Differential Geometry: A Symposium in Honor of Manfredo Do Carmo, Wiley, 1991, pp. 311-320. | MR | Zbl

[17] Struwe M., Variational Methods: Applications to Nonlinear PDE & Hamiltonian Systems, Springer-Verlag, Berlin, 1990. | MR | Zbl

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