Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 2, pp. 341-358. 
@article{AIHPC_2003__20_2_341_0,
     author = {Silva, Elves A. B. and Xavier, Magda S},
     title = {Multiplicity of solutions for quasilinear elliptic problems involving critical {Sobolev} exponents},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {341--358},
     publisher = {Elsevier},
     volume = {20},
     number = {2},
     year = {2003},
     doi = {10.1016/S0294-1449(02)00013-6},
     mrnumber = {1961520},
     zbl = {1030.35081},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0294-1449(02)00013-6/}
}
TY  - JOUR
AU  - Silva, Elves A. B.
AU  - Xavier, Magda S
TI  - Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2003
SP  - 341
EP  - 358
VL  - 20
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/S0294-1449(02)00013-6/
DO  - 10.1016/S0294-1449(02)00013-6
LA  - en
ID  - AIHPC_2003__20_2_341_0
ER  - 
%0 Journal Article
%A Silva, Elves A. B.
%A Xavier, Magda S
%T Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
%J Annales de l'I.H.P. Analyse non linéaire
%D 2003
%P 341-358
%V 20
%N 2
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/S0294-1449(02)00013-6/
%R 10.1016/S0294-1449(02)00013-6
%G en
%F AIHPC_2003__20_2_341_0
Silva, Elves A. B.; Xavier, Magda S. Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 2, pp. 341-358. doi : 10.1016/S0294-1449(02)00013-6. http://archive.numdam.org/articles/10.1016/S0294-1449(02)00013-6/

[1] Alves C.O., Gonçalves J.V., Existence of positive solutions for m-Laplacian equations RN involving critical Sobolev exponents, Nonlinear Anal. TMA 32 (1998) 53-70. | MR | Zbl

[2] Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973) 349-381. | MR | Zbl

[3] Ambrosetti A., Struwe M., A note on the problem −Δu=λu+u|u|2∗−2, Manuscripta Math. 54 (1986) 373-379. | Zbl

[4] Anane A., Simplicité et isolation de la première valeur propre du p-Laplacien avec poids, C. R. Acad. Sci. Paris, Ser. I 305 (1987) 725-728. | MR | Zbl

[5] Bartolo P., Benci V., Fortunato D., Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. TMA 7 (9) (1983) 981-1012. | Zbl

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

[7] Capozzi A., Fortunato D., Palmieri G., An existence result for nonlinear elliptic problems involving critical Sobolev exponent, Ann. Inst. H. Poincaré, Analyse Non Linéaire 2 (6) (1985) 463-470. | Numdam | MR | Zbl

[8] Cerami G., Fortunato D., Struwe M., Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents, Ann. Inst. H. Poincaré, Analyse Non Linéaire 1 (1984) 341-350. | Numdam | MR | Zbl

[9] Costa D.G., Silva E.A.B., A note on problems involving critical Sobolev exponents, Differential and Integral Equations 8 (3) (1995) 673-679. | MR | Zbl

[10] Defigueiredo D.G., The Ekeland Variational Principle with Applications and Detours, Springer-Verlag, New York, 1989.

[11] Drábek P., Huang Y.X., Multiplicity of positive solutions for some quasilinear elliptic equation in RN with critical Sobolev exponent, J. Differential Equations 140 (1997) 106-132. | MR | Zbl

[12] Folland G.B., Real Analysis, Wiley, 1984. | MR | Zbl

[13] Fucik S., John O., Necas J., On the existence of Schauder basis in Sobolev spaces, Comment. Math. Univ. Carolin. 13 (1972) 163-175. | MR | Zbl

[14] Garcia Azorero J., Peral Alonso I., Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term, Trans. Amer. Math. Soc. 323 (2) (1991) 877-895. | MR | Zbl

[15] Ghoussoub N., Yuan C., Multiple solutions for quasilinear PDES involving the critical Sobolev and Hardy exponents, Trans. Amer. Math. Soc. 352 (12) (2000) 5703-5743. | MR | Zbl

[16] Guedda M., Veron L., Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA 13 (8) (1989) 879-902. | MR | Zbl

[17] Gazzola F., Ruf B., Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations, Advances in Differential Equations 2 (4) (1997) 555-572. | MR | Zbl

[18] Lindenstrauss J., Tzafriri L., Classical Banach Spaces I, Springer-Verlag, Berlin, 1977. | MR | Zbl

[19] Lions P.L., The concentration-compactness principle in the calculus of variations. The limit case, part 1, 2, Rev. Mat. Iberoamericana 1 (1985) 145-201, pp. 45-121. | MR | Zbl

[20] Marti J.T., Introduction to the Theory of Bases, Springer-Verlag, New York, 1969. | MR | Zbl

[21] Rabinowitz P.H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math., 65, AMS, Providence, RI, 1986. | MR | Zbl

[22] E.A.B. Silva, Critical point theorems and applications to differential equations, Ph.D. Thesis, University of Wisconsin-Madison, 1988.

[23] Silva E.A.B., Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Anal. TMA 16 (1991) 455-477. | MR | Zbl

[24] Silva E.A.B., Soares S.H.M., Quasilinear Dirichlet problems in RN with critical growth, Nonlinear Anal. TMA 43 (2001) 1-20. | MR | Zbl

[25] Wei Z., Wu X., A multiplicity result for quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA 18 (6) (1992) 559-567. | MR | Zbl

Cité par Sources :