On nonhomogeneous elliptic equations involving critical Sobolev exponent

G. Tarantello

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 3, page 281-304
  • ISSN: 0294-1449

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Tarantello, G.. "On nonhomogeneous elliptic equations involving critical Sobolev exponent." Annales de l'I.H.P. Analyse non linéaire 9.3 (1992): 281-304. <http://eudml.org/doc/78280>.

@article{Tarantello1992,
author = {Tarantello, G.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {semilinear elliptic equation; critical Sobolev exponent; homogeneous Dirichlet problem; number of solutions},
language = {eng},
number = {3},
pages = {281-304},
publisher = {Gauthier-Villars},
title = {On nonhomogeneous elliptic equations involving critical Sobolev exponent},
url = {http://eudml.org/doc/78280},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Tarantello, G.
TI - On nonhomogeneous elliptic equations involving critical Sobolev exponent
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 3
SP - 281
EP - 304
LA - eng
KW - semilinear elliptic equation; critical Sobolev exponent; homogeneous Dirichlet problem; number of solutions
UR - http://eudml.org/doc/78280
ER -

References

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  1. [A.R.] A. Ambrosetti and P. Rabinowitz, Dual Variational Methods in Critical Point Theory and Applications, J. Funct. Anal., Vol. 11, 1973, pp. 349-381. Zbl0273.49063MR370183
  2. [A.E.] J.P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Pure and Applied Mathem- atics, Wiley Interscience Publications, 1984. Zbl0641.47066MR749753
  3. [B] H. Brezis, Some Variational Problems with Lack of Compactness, Proc. Symp. Pure Math., Vol. 45, part 1, F. BROWER Ed., Amer. Math. Soc., 1986, pp. 165-201. Zbl0617.35041MR843559
  4. [B.L.] H. Brezis and T. Kato, Remarks on the Schrodinger Operator with Singular Complex Potential, J. Math. Pure Appl., 58, 1979, pp. 137-151. Zbl0408.35025MR539217
  5. [B.K.] H. Brezis et E. Lieb, A Relations Between Pointwise Convergence of Functions and Convergence of Integrals, Proc. Amer. Math. Soc., Vol. 88, 1983, pp. 486-490. Zbl0526.46037MR699419
  6. [B.N.1] H. Brezis et L. Nirenberg, A Minimization Problem with Critical Exponent and Non Zero Data, in "Symmetry in Nature", Scuola Norm. Sup. Pisa, 1989, pp. 129-140. Zbl0763.46023
  7. [B.N.2] H. Brezis et L. Nirenberg, Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents, Comm. Pure Appl. Math., Vol. 36, 1983, pp. 437-477. Zbl0541.35029MR709644
  8. [C.S.] L. Caffarelli et J. Spruck, Variational Problems with Critical Growth and Positive Dirichlet Data (to appear). Zbl0717.35028
  9. [C.R.] M. Crandall et P. Rabinowitz, Some Continuation and Variational Method for Positive Solutions of Nonlinear Elliptic Eigenvalue Problems, Arch. Rational Mech. Anal., Vol. 58, 1975, pp. 207-218. Zbl0309.35057MR382848
  10. [F] G. Folland, Real Analysis, Wiley Interscience, N.Y., 1984. Zbl0549.28001MR767633
  11. [G.P.] N. Ghoussoub et D. Preiss, A General Mountain Pass Principle for Locating and Classifying Critical Point, Ann. I.H.P.Analyse non linéaire, Vol. 6, n° 5, 1989. pp. 321-330. Zbl0711.58008MR1030853
  12. [H.] H. Hofer, A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain Pass Theorem, J. London Math. Soc., Vol. 31, 1985, pp. 566-570. Zbl0573.58007MR812787
  13. [M.] F. Merle, Sur la non-existence de solutions positives d'équations elliptiques surlinéaires, C. R. Acad. Sci. Paris, T. 306, Serie I, 1988, pp. 313-316. Zbl0696.35062MR932345
  14. [P.] S. Pohozaev, Eigenfunctions of the Equation Δu+λf(u)=0, Soviet Math. Dokl.. Vol. 6, 1965, pp. 1408-1411. Zbl0141.30202MR192184
  15. [R.] O. Rey, Concentration of Solutions to Elliptic Equations with CriticalNonlinearity (submitted). Zbl0761.35034
  16. [S.] M. Struwe, Variational Methods and their Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Lecture notes E.T.H., Zurich, 1989. 
  17. [T.] G.. Talenti, Best Constant in Sobolev Inequality, Ann. Mat. Pure Appl., Vol. 110. 1976, pp. 353-372. Zbl0353.46018MR463908
  18. [Z.] X. Zheng, A Nonexistence Result of Positive Solutions for an Elliptic Equation. Ann. I.H.P.Analyse nonlinéaire, Vol. 7, n° 2, 1990, pp. 91-96. Zbl0719.35028MR1051229

Citations in EuDML Documents

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  1. Elliot Tonkes, Solutions to a perturbed critical semilinear equation concerning the N -Laplacian in N
  2. Paul A. Binding, Pavel Drábek, Yin Xi Huang, Positive solutions of critical quasilinear elliptic equations in R N
  3. Daomin Cao, Ezzat S. Noussair, Multiplicity of positive and nodal solutions for nonlinear elliptic problems in N
  4. Boumediene Abdellaoui, Veronica Felli, Ireneo Peral, Existence and nonexistence results for quasilinear elliptic equations involving the p -Laplacian

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