Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
Silva, Elves A. B. ; Xavier, Magda S
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 341-358 / Harvested from Numdam
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@article{AIHPC_2003__20_2_341_0,
     author = {Silva, Elves A. de 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},
     volume = {20},
     year = {2003},
     pages = {341-358},
     doi = {10.1016/S0294-1449(02)00013-6},
     mrnumber = {1961520},
     zbl = {1030.35081},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 341-358. doi : 10.1016/S0294-1449(02)00013-6. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_2_341_0/

[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 1491613 | Zbl 0892.35062

[2] Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973) 349-381. | MR 370183 | Zbl 0273.49063

[3] Ambrosetti A., Struwe M., A note on the problem −Δu=λu+u|u|2∗−2, Manuscripta Math. 54 (1986) 373-379. | Zbl 0596.35043

[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 920052 | Zbl 0633.35061

[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 0522.58012

[6] Brézis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983) 437-477. | MR 709644 | Zbl 0541.35029

[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 831041 | Zbl 0612.35053

[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 779872 | Zbl 0568.35039

[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 1306583 | Zbl 0812.35046

[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 1473856 | Zbl 0902.35035

[12] Folland G.B., Real Analysis, Wiley, 1984. | MR 767633 | Zbl 0924.28001

[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 306890 | Zbl 0231.46064

[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 1083144 | Zbl 0729.35051

[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 1695021 | Zbl 0956.35056

[16] Guedda M., Veron L., Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA 13 (8) (1989) 879-902. | MR 1009077 | Zbl 0714.35032

[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 1441856 | Zbl 1023.35508

[18] Lindenstrauss J., Tzafriri L., Classical Banach Spaces I, Springer-Verlag, Berlin, 1977. | MR 500056 | Zbl 0852.46015

[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 850686 | Zbl 0704.49005

[20] Marti J.T., Introduction to the Theory of Bases, Springer-Verlag, New York, 1969. | MR 438075 | Zbl 0191.41301

[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 845785 | Zbl 0609.58002

[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 1093380 | Zbl 0731.35042

[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 1784441 | Zbl 01539287

[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 1154480 | Zbl 0762.35034