On the existence of a positive solution of semilinear elliptic equations in unbounded domains

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 14, Issue 3, 1997, Pages 365-413

  Bahri, Abbas ^a   Lions, Pierre Louis ^a  

^a NONE

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EID: 0000255012     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(97)80142-4     Document Type: Article

References (46)

1. A. BAHRI, Pseudo-Orbits of contact forms, Pitman Research Notes in Mathematics, Longman London, Vol. 173.
2. A. BAHRI, Critical points at infinity in some variational problems, Pitman Research Notes in mathematics, Longman, London, Vol. 182.
3. A. BAHRI, Topological results on a certain class of functionals and applications, J. Funct. Anal., Vol. 41, 1981, pp. 397-427.
4. A. BAHRI and H. BERESTYCKI, A perturbation method in critical point theory and applications. Trans. Amer. Math. Soc., Vol. 297, 1987, pp. 1-32.
5. A. BAHRI and J. M. CORON, On a non-linear ellepttic equation involving the critical Sobolev exponent; the effect of the topology of the domain, Comm. Pure and Appl. Math., Vol. 41, 1988, pp. 253-294.
6. V. BENCI and G. CERAMI, Positive solutions of semilinear elliptic problems in exterior domains. Preprint.
7. H. BERESTYCKI and P.-L. LIONS, Nonlinear scalar fields equations, Arch. Rat. Mech. Anal., Vol. I 82, 1983, pp. 313-346; Vol. II 82, 1983, pp. 347-376.
8. H. BERESTYCKI and P.-L. LIONS, Nonlinear scalar fields equations, Arch. Rat. Mech. Anal., Vol. I 82, 1983, pp. 313-346; Vol. II 82, 1983, pp. 347-376.
9. M. BERGER, On the existence and structure of stationary states for a nonlinear Klein-Gordon equation, J. Funct. Anal., Vol. 9, 1972, pp. 249-261.
10. G. BREDON, Introduction to Compact transformation Groups, New York-Academic Press, 1972.
11. H. BREZIS and J. M. CORON, convergence of solutions of H-systems or how to blow bubbles, Arch. Rational Mech. Anal., Vol. 89, 1985, pp. 21-56.
12. 3 = 0 and a variational characterization of other solutions, Arch. Rat. Mech. Anal., Vol. 46, 1982, pp. 81-95.
13. C. V. COFFMAN and M. MARCUS, personal communication.
14. C. V. COFFMAN and M. MARCUS, Existence theorems for superlinear elliptic Dirichlet problems in exterior domains, Nonlinear Analysis and Its Applications, Part 2, Vol. 45; AMS, Providence, 1983.
15. S. COLEMAN, V. GLASER and A. MAWHIN, Action minima among solutions to a class of Euclidian scalar field equations, Comm. Math. Phys., Vol. 58, 1978, pp. 211-221.
16. J. M. CORON, Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris, I, Vol. 299, 1984, pp. 209-212.
17. W. Y. DING and W. M. NI, On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Rat. Mech Anal.
18. I. EKELAND, Nonconvex minimization problems, Bull. Amer. Math. Soc., Vol. I, 1979, pp. 443-479.
19. M. J. ESTEBAN and P.-L. LIONS, Existence and nonexistence results for semilinear elliptic problems in unbounded domains, Proc. Roy. Soc. Edim, Vol. 93, 1982, pp. 1-14; C. R. Acad. Sci. Paris, Vol. 290, 1980, pp. 1083-1085.
20. M. J. ESTEBAN and P.-L. LIONS, Existence and nonexistence results for semilinear elliptic problems in unbounded domains, Proc. Roy. Soc. Edim, Vol. 93, 1982, pp. 1-14; C. R. Acad. Sci. Paris, Vol. 290, 1980, pp. 1083-1085.
21. M. J. ESTEBAN and P.-L. LIONS, Γ-convergence and the concentration-compactness method for some variational problems with lack of compactness. Preprint.
22. B. GIDAS, W. M. NI and L. NIRENBERG, Symmetry and related properties via the maximum principle, Comm. Math. Phys., Vol. 68, 1979, pp. 209-243.
23. n, Advances in Math. Supplementary Studies, Vol. 7, 1981, pp. 369-402.
24. n , Arch. Rat. Mech. Anal., Vol. 105, 1985, pp. 243-266.
25. P.-L. LIONS, The concentration-compactness principle in the Calculus of Variations, The locally compact case, Ann. Inst. H. Poincaré, Vol. I 1, 1984, pp. 109-145; Vol. II 1, 1984, pp. 223-283,
26. P.-L. LIONS, The concentration-compactness principle in the Calculus of Variations, The locally compact case, Ann. Inst. H. Poincaré, Vol. I 1, 1984, pp. 109-145; Vol. II 1, 1984, pp. 223-283,
27. see also, C. R. Acad. Sci. Paris 294, Vol. 1, pp. 223-283; 1982, pp. 261-264; Contributions to nonlinear partial differential equations, Pitman, London 1983.
28. see also, C. R. Acad. Sci. Paris 294, Vol. 1, pp. 223-283; 1982, pp. 261-264; Contributions to nonlinear partial differential equations, Pitman, London 1983.
29. see also, C. R. Acad. Sci. Paris 294, Vol. 1, pp. 223-283; 1982, pp. 261-264; Contributions to nonlinear partial differential equations, Pitman, London 1983.
30. P.-L. LIONS, On positive solutions of semilinear elliptic equations in unbounded domains. Preprint.
31. P.-L. LIONS, Solutions of Hartree-Fock equations for Coulomb systems, Comm. Math. Phys.
32. P.-L. LIONS, Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal., Vol. 49, 1982, pp. 315-334.
33. 1, J. Funct. Anal., Vol. 49, 1982, pp. 315-334.
34. P.-L. LIONS, The concentration-compactness principle in the Calculus of Variations. The limit case, Riv. Mat. Ibereamericana, Vol. I 1, 1985, pp. 145-201; Vol. II 1, 1985, pp. 45-121;
35. P.-L. LIONS, The concentration-compactness principle in the Calculus of Variations. The limit case, Riv. Mat. Ibereamericana, Vol. I 1, 1985, pp. 145-201; Vol. II 1, 1985, pp. 45-121;
36. see also Seminaire, Goulaouic-Meyer-Schwartz, 1982-1983, exposé XIV, École Polytechnique, Palaiseau and C. R. Acad. Sci. Paris; 296, 1983, pp. 645-648.
37. K. MAC LEOD and J. SERRIN, Uniqueness of solutions of semilinear Poisson equations, Proc. Nat. Acad. Sci. USA, Vol. 78, 1981, pp. 6592-6585.
38. MILNOR, Morse theory, Annals of Mathematical Studies, Princeton Univ. Press, Study No. 52.
39. Z. NEHARI, On a nonlinear differential equation arising in nuclear physics, Proc. Roy. Irish Acad., Vol. 62, 1963, pp. 117-135.
40. P. H. RABINOWITZ, Variational methods for nonlinear eigenvalue problems. In Eigenvalues of Nonlinear Problems, Edis. Cremonese, Rome, 1972.
41. G. H. RYDER, Boundary value problems for a class of nonlinear differential equations, Proc. J. Math., Vol. 22, 1967, pp. 477-503.
42. P. SAKS and K. UHLENBECK, The existence of minimal immersions of 2-sphere, Ann. Math., Vol. 113, 1981, pp. 1-24.
43. W. STRAUSS, Existence of solitary vaves in higher dimensions, Comm. Math. Phys., Vol. 55, 1977, pp. 149-162.
44. M. STRUWE, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. Vol. 187, 1984, pp. 511-517.
45. 3 I, Comm. Math. Physics, Vol. 86, 1982, pp. 257-298.
46. 3 II, Comm. Math. Physics, Vol. 86, 1982, pp. 299-320.