Multiple positive solutions for singularly perturbed elliptic problems in exterior domains
Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 5, p. 759-777
@article{AIHPC_2003__20_5_759_0,
     author = {Cerami, Giovanna and Molle, Riccardo},
     title = {Multiple positive solutions for singularly perturbed elliptic problems in exterior domains},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {20},
     number = {5},
     year = {2003},
     pages = {759-777},
     doi = {10.1016/S0294-1449(02)00030-6},
     zbl = {01975933},
     mrnumber = {1995501},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2003__20_5_759_0}
}
Cerami, Giovanna; Molle, Riccardo. Multiple positive solutions for singularly perturbed elliptic problems in exterior domains. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 5, pp. 759-777. doi : 10.1016/S0294-1449(02)00030-6. http://www.numdam.org/item/AIHPC_2003__20_5_759_0/

[1] Bahri A., Lions P.L., On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (3) (1997) 365-413. | Numdam | MR 1450954 | Zbl 0883.35045

[2] Bahri A., Li Y.Y., On a min-max procedure for the existence of a positive solution for certain scalar field equations in RN, Rev. Mat. Iberoamericana 6 (1-2) (1990) 1-15. | MR 1086148 | Zbl 0731.35036

[3] Benci V., Cerami G., Positive solutions of some nonlinear elliptic problems in exterior domains, Arch. Rational Mech. Anal. 99 (1987) 283-300. | MR 898712 | Zbl 0635.35036

[4] Benci V., Cerami G., Existence of positive solutions of the equation −Δu+a(x)u=u(N+2)/(N−2) in RN, J. Funct. Anal. 88 (1) (1990) 90-117. | Zbl 0705.35042

[5] Berestycki H., Lions P.L., Nonlinear scalar fields equations - I. Existence of a ground-state, Arch. Rational Mech. Anal. 82 (1983) 313-346. | MR 695535 | Zbl 0533.35029

[6] Cerami G., Maniscalco C., Multiple positive solutions for a singularly perturbed Dirichlet problem in “geometrically trivial” domains, Topol. Methods Nonlin. Anal. 19 (1) (2002) 63-76. | Zbl 1094.35501

[7] Cerami G., Passaseo D., Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology, Nonlinear Analysis TMA 18 (2) (1992) 109-119. | Zbl 0810.35024

[8] Cerami G., Passaseo D., Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains, Nonlinear Analysis TMA 24 (11) (1995) 1533-1547. | MR 1328581 | Zbl 0845.35026

[9] G. Cerami, D. Passaseo, Effect of concentrating potentials in some singularly perturbed problems, Calculus of Variations and PDE, to appear. | MR 1989833 | Zbl 01969061

[10] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in RN, in: Mathematical Analysis and Applications, Part A, Advances in Mathematics Supplementary Studies, 7-A, Academic Press, 1981, pp. 369-402. | MR 634248 | Zbl 0469.35052

[11] Grossi M., Passaseo D., Nonlinear elliptic Dirichlet problems in exterior domains: the role of geometry and topology of the domain, Comm. Appl. Nonlinear Anal. 2 (2) (1995) 1-31. | MR 1326704 | Zbl 0863.35035

[12] Kwong M.K., Uniqueness of positive solutions of Δuu+up=0, Arch. Rational Mech. Anal. 105 (1989) 243-266. | Zbl 0676.35032

[13] Molle R., Musso M., Passaseo D., Positive solutions for a class of nonlinear elliptic problems in RN, Proc. Roy. Soc. Edinburgh Sect. A 130 (1) (2000) 141-166. | MR 1742584 | Zbl 0947.35062

[14] Molle R., Passaseo D., On the behaviour of the solutions for a class of nonlinear elliptic problems in exterior domains, Discrete Contin. Dynam. Systems 4 (3) (1998) 445-454. | MR 1612740 | Zbl 0951.35052

[15] Molle R., Passaseo D., Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains, Nonlinear Anal. Ser. A: Theory Methods 39 (4) (2000) 447-462. | MR 1725399 | Zbl 0939.35071

[16] Strauss W.A., Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977) 149-162. | MR 454365 | Zbl 0356.35028

[17] Struwe M., Variational Methods - Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 1990. | MR 1078018 | Zbl 0746.49010