Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents

Elves A. B. Silva; Magda S Xavier

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 2, page 341-358
  • ISSN: 0294-1449

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Silva, Elves A. B., and Xavier, Magda S. "Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents." Annales de l'I.H.P. Analyse non linéaire 20.2 (2003): 341-358. <http://eudml.org/doc/78582>.

@article{Silva2003,
author = {Silva, Elves A. B., Xavier, Magda S},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {-Laplacian operator; quasilinear elliptic equation; critical Sobolev exponent; critical growth; Palais-Smale condition},
language = {eng},
number = {2},
pages = {341-358},
publisher = {Elsevier},
title = {Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents},
url = {http://eudml.org/doc/78582},
volume = {20},
year = {2003},
}

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
PB - Elsevier
VL - 20
IS - 2
SP - 341
EP - 358
LA - eng
KW - -Laplacian operator; quasilinear elliptic equation; critical Sobolev exponent; critical growth; Palais-Smale condition
UR - http://eudml.org/doc/78582
ER -

References

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  1. [1] Alves C.O., Gonçalves J.V., Existence of positive solutions for m-Laplacian equations RN involving critical Sobolev exponents, Nonlinear Anal. TMA32 (1998) 53-70. Zbl0892.35062MR1491613
  2. [2] Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal.14 (1973) 349-381. Zbl0273.49063MR370183
  3. [3] Ambrosetti A., Struwe M., A note on the problem −Δu=λu+u|u|2∗−2, Manuscripta Math.54 (1986) 373-379. Zbl0596.35043
  4. [4] Anane A., Simplicité et isolation de la première valeur propre du p-Laplacien avec poids, C. R. Acad. Sci. Paris, Ser. I305 (1987) 725-728. Zbl0633.35061MR920052
  5. [5] Bartolo P., Benci V., Fortunato D., Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity, Nonlinear Anal. TMA7 (9) (1983) 981-1012. Zbl0522.58012
  6. [6] Brézis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math.36 (1983) 437-477. Zbl0541.35029MR709644
  7. [7] Capozzi A., Fortunato D., Palmieri G., An existence result for nonlinear elliptic problems involving critical Sobolev exponent, Ann. Inst. H. Poincaré, Analyse Non Linéaire2 (6) (1985) 463-470. Zbl0612.35053MR831041
  8. [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 Linéaire1 (1984) 341-350. Zbl0568.35039MR779872
  9. [9] Costa D.G., Silva E.A.B., A note on problems involving critical Sobolev exponents, Differential and Integral Equations8 (3) (1995) 673-679. Zbl0812.35046MR1306583
  10. [10] DeFigueiredo D.G., The Ekeland Variational Principle with Applications and Detours, Springer-Verlag, New York, 1989. 
  11. [11] Drábek P., Huang Y.X., Multiplicity of positive solutions for some quasilinear elliptic equation in RN with critical Sobolev exponent, J. Differential Equations140 (1997) 106-132. Zbl0902.35035MR1473856
  12. [12] Folland G.B., Real Analysis, Wiley, 1984. Zbl0924.28001MR767633
  13. [13] Fucik S., John O., Necas J., On the existence of Schauder basis in Sobolev spaces, Comment. Math. Univ. Carolin.13 (1972) 163-175. Zbl0231.46064MR306890
  14. [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. Zbl0729.35051MR1083144
  15. [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. Zbl0956.35056MR1695021
  16. [16] Guedda M., Veron L., Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA13 (8) (1989) 879-902. Zbl0714.35032MR1009077
  17. [17] Gazzola F., Ruf B., Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations, Advances in Differential Equations2 (4) (1997) 555-572. Zbl1023.35508MR1441856
  18. [18] Lindenstrauss J., Tzafriri L., Classical Banach Spaces I, Springer-Verlag, Berlin, 1977. Zbl0852.46015MR500056
  19. [19] Lions P.L., The concentration-compactness principle in the calculus of variations. The limit case, part 1, 2, Rev. Mat. Iberoamericana1 (1985) 145-201, pp. 45–121. Zbl0704.49005MR850686
  20. [20] Marti J.T., Introduction to the Theory of Bases, Springer-Verlag, New York, 1969. Zbl0191.41301MR438075
  21. [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. Zbl0609.58002MR845785
  22. [22] E.A.B. Silva, Critical point theorems and applications to differential equations, Ph.D. Thesis, University of Wisconsin-Madison, 1988. 
  23. [23] Silva E.A.B., Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Anal. TMA16 (1991) 455-477. Zbl0731.35042MR1093380
  24. [24] Silva E.A.B., Soares S.H.M., Quasilinear Dirichlet problems in RN with critical growth, Nonlinear Anal. TMA43 (2001) 1-20. Zbl1158.35368MR1784441
  25. [25] Wei Z., Wu X., A multiplicity result for quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA18 (6) (1992) 559-567. Zbl0762.35034MR1154480

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