Blow-up and nonexistence of sign changing solutions to the Brezis–Nirenberg problem in dimension three
Mohamed Ben Ayed; Khalil El Mehdi[1]; Filomena Pacella
- [1] Université de Nouakchott Faculté des Sciences et Techniques BP 5026, Nouakchott MAURITANIA
Annales de l'I.H.P. Analyse non linéaire (2006)
- Volume: 23, Issue: 4, page 567-589
- ISSN: 0294-1449
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topBen Ayed, Mohamed, El Mehdi, Khalil, and 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 23.4 (2006): 567-589. <http://eudml.org/doc/78702>.
@article{BenAyed2006,
affiliation = {Université de Nouakchott Faculté des Sciences et Techniques BP 5026, Nouakchott MAURITANIA},
author = {Ben Ayed, Mohamed, El Mehdi, Khalil, Pacella, Filomena},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {blow-up analysis; sign changing solutions; nodal domains; critical exponent},
language = {eng},
number = {4},
pages = {567-589},
publisher = {Elsevier},
title = {Blow-up and nonexistence of sign changing solutions to the Brezis–Nirenberg problem in dimension three},
url = {http://eudml.org/doc/78702},
volume = {23},
year = {2006},
}
TY - JOUR
AU - Ben Ayed, Mohamed
AU - El Mehdi, Khalil
AU - Pacella, Filomena
TI - Blow-up and nonexistence of sign changing solutions to the Brezis–Nirenberg problem in dimension three
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 4
SP - 567
EP - 589
LA - eng
KW - blow-up analysis; sign changing solutions; nodal domains; critical exponent
UR - http://eudml.org/doc/78702
ER -
References
top- [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. Zbl0806.35031MR1288602
- [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. I306 (1988) 711-714. Zbl0696.35059MR944417
- [3] Atkinson F.V., Brezis H., Peletier L.A., Nodal solutions of elliptic equations with critical Sobolev exponents, J. Differential Equations85 (1990) 151-170. Zbl0702.35099MR1052332
- [4] Bahri A., Critical Points at Infinity in Some Variational Problems, Pitman Res. Notes Math. Ser., vol. 182, Longman Sci. Tech., Harlow, 1989. Zbl0676.58021MR1019828
- [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 Linéaire19 (2002) 715-744. Zbl1130.35335MR1922475
- [6] Brezis H., Some variational problems with lack of compactness, Proc. Sympos. Pure Math.45 (1986) 165-201. Zbl0617.35041MR843559
- [7] Brezis H., Kato T., Remarks on the Schroedinger operator with singular complex potential, J. Math. Pures Appl.58 (1979) 137-151. Zbl0408.35025MR539217
- [8] Brezis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math.36 (1983) 437-477. Zbl0541.35029MR709644
- [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. Zbl0702.35085MR982351
- [10] Clapp M., Weth T., Multiple solutions for the Brezis–Nirenberg problem, Adv. Differential Equations10 (2005) 463-480. Zbl1284.35151MR2122698
- [11] Druet O., Elliptic equations with critical Sobolev exponent in dimension 3, Ann. Inst. H. Poincaré Anal. Non Linéaire19 (2002) 125-142. Zbl1011.35060MR1902741
- [12] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, Springer-Verlag, Berlin, 1977. Zbl0361.35003MR473443
- [13] Li Y.Y., Prescribing scalar curvature on and related topics, Part I, J. Differential Equations120 (1995) 319-410. Zbl0827.53039MR1347349
- [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. Zbl0786.35059MR1040954
- [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. Zbl0702.49038MR994021
- [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. Zbl0733.53021MR1173050
- [17] Struwe M., Variational Methods: Applications to Nonlinear PDE & Hamiltonian Systems, Springer-Verlag, Berlin, 1990. Zbl0746.49010MR1078018
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