Rocky Mountain Journal of Mathematics

Existence and Multiplicity Results for a Class of Elliptic Problems with Critical Sobolev Exponents

D. Costa and G. Liao

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 21, Number 4 (1991), 1207-1223.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072904

Digital Object Identifier
doi:10.1216/rmjm/1181072904

Mathematical Reviews number (MathSciNet)
MR1147857

Zentralblatt MATH identifier
0802.35046

Citation

Costa, D.; Liao, G. Existence and Multiplicity Results for a Class of Elliptic Problems with Critical Sobolev Exponents. Rocky Mountain J. Math. 21 (1991), no. 4, 1207--1223. doi:10.1216/rmjm/1181072904. https://projecteuclid.org/euclid.rmjm/1181072904


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References

  • T. Aubin, Nonlinear analysis on manifolds. Monge-Ampére equations,\noindent Springer-Verlag, New York, Heidelberg, Berlin, 1982.
  • A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
  • M.S. Berger, Nonlinearity and functional analysis, Academic Press, New York, 1977.
  • P. Bartolo, V. Benci, and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with Strong resonance at infinity, J. Nonlinear Anal. T.M.A. 7 (1983), 981-1012.
  • H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477.
  • A. Capozzi, D. Fortunato and G. Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponents, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear).
  • G. Cerami, D. Fortunato and M. Struwe, Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents, Ann. Inst. H. Poincaré 1 (1984), 341-350.
  • J.F. Escobar, Positive solutions for some semilinear elliptic equations with critical Sobolev exponents, preprint.
  • J.F. Escobar and R. Schoen, Conformal metrics with prescribed scalar curvature, Invent. Math. 86 (1986), 243-254.
  • E.W.C. van Groesen, Applications of natural constraints in critical point theory to periodic solutions of natural Hamiltonian systems, MRC Technical Report #2593, 1983.
  • R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479-495.
  • N. Trudinger, Remarks concerning the conformal deformation of Riemannian structure on compact manifolds, Ann. Sc. Norm. Sup. Pisa, 22, 1968, p. 265-274.
  • H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21-27.