References
Ambrosetti, A., & Rabinowitz, P. H., Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973), 349–381.
Bahri, A., & Coron, J. M., Sur une équation elliptique avec l'exposant critique de Sobolev. C. R. Acad. Sc. Paris 301 (1985), 345–348, and detailed paper to appear.
Benci, V., & Cerami, G. In preparation.
Benci, V., & Fortunato, D., Some compact embedding theorems for weighted Sobolev spaces. Boll. U. M. I. (5), 13 B (1976), 832–843.
Berestycki, H., & Lions, P. L., Nonlinear scalar field equations. I. Existence of a ground state. Arch. Rational Mech. Anal. 82 (1983), 313–346.
Berestycki, H., & Lions, P. L., Nonlinear scalar field equations. II. Existence of infinitely many solutions. Arch. Rational Mech. Anal. 82 (1983), 347–376.
Brezis, H., & Lieb, E., A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer. Math. Soc. 88 (1983), 486–490.
Coffman, C. V., Uniqueness of the ground state solution for Δu − u + u 3 = 0 and a variational characterization of the other solutions. Arch. Rational Mech. Anal. 46 (1972), 81–85.
Coffman, C. V., & Marcus, M. M., Existence theorems for superlinear elliptic Dirichlet problems in exterior domains. Preprint.
Coron, J. M., Topologie et cas limite des injections de Sobolev. C. R. Acad. Sci. Paris 299 (1984), 209–212.
Esteban, M. J., & Lions, P. L., Existence and non-existence results for semilinear elliptic problems in unbounded domains. Proc. Royal Edinbourgh Soc. 93 A (1982), 1–14.
Gidas, B., Ni, W. M., & Nirenberg, L., Symmetry of positive solutions of nonlinear elliptic equations in ℝN. Mathematical Analysis and Applications, Part A, Advances in Mathematics Supplementary Studies, vol. 7 A, Academic Press (1981).
Hempel, J. A., Multiple solutions for a class of nonlinear boundary value problems. Indiana Univ. Math. J. 20 (1971), 983–996.
Hofer, H., Variational and topological methods in partially ordered Hilbert spaces. Math. Ann. 261 (1982), 493–514.
Lions, P. L., La méthode de concentration-compacité en calcul de variations. Séminaire Goulaouic-Meyer-Schwartz 1982–83, Exposé XIV, (Février 1983). École Polytechnique Palaiseau.
Lions, P. L., The concentration-compactness principle in the Calculus of Variations —The locally compact case—Part I. Ann. Inst. H. Poincaré—Analyse Nonlinéaire 1 (1984), 109–145.
Lions, P. L., The concentration-compactness principle in the Calculus of Variations. The locally compact case. Part II. Ann. Inst. H. Poincaré. Analyse Nonlinéaire 1 (1984), 223–283.
Lions, P. L., Solutions of Hartree-Fock equations for Coulomb systems. Preprint n. 8607 CEREMADE.
McLeod, K., & Serrin, J., Uniqueness of solutions of semilinear Poisson equations. Proc. Natl. Acad. Sci. U. S. A. 78, n. 11 (1981), 6592–6595.
Pohožaev, S., Eigenfunctions of the equation Δu + λf(u). Soviet Math. Doklady 6 (1965), 1408–1411.
Rabinowitz, P. H., Variational methods for nonlinear eigenvalue problems, Eigenvalues of Nonlinear Problems. (G. Prodi, Ed.), C. I. M. E., Edizioni Cremonese, Roma, 1975, 141–195.
Rabinowitz, P. H., Théorie du degré topologique et applications à des problèmes aux limites nonlinéaires. Notes. Lab. Analyse Numerique, Un. Paris VI, n. 75010 (1975).
Strauss, W. A., Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55 (1977), 149–162.
Struwe, M., A global compactness result for elliptic boundary value problems involving limiting nonlinearities. Math. Z. 187 (1984), 511–517.
Author information
Authors and Affiliations
Additional information
Communicated by H. Brezis
Rights and permissions
About this article
Cite this article
Benci, V., Cerami, G. Positive solutions of some nonlinear elliptic problems in exterior domains. Arch. Rational Mech. Anal. 99, 283–300 (1987). https://doi.org/10.1007/BF00282048
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00282048