Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary
Annales de l'I.H.P. Analyse non linéaire, Volume 24 (2007) no. 1, p. 41-60
@article{AIHPC_2007__24_1_41_0,
     author = {Cerami, Giovanna and Molle, Riccardo and Passaseo, Donato},
     title = {Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {24},
     number = {1},
     year = {2007},
     pages = {41-60},
     doi = {10.1016/j.anihpc.2005.09.007},
     zbl = {1123.35017},
     mrnumber = {2286558},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2007__24_1_41_0}
}
Cerami, Giovanna; Molle, Riccardo; Passaseo, Donato. Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary. Annales de l'I.H.P. Analyse non linéaire, Volume 24 (2007) no. 1, pp. 41-60. doi : 10.1016/j.anihpc.2005.09.007. http://www.numdam.org/item/AIHPC_2007__24_1_41_0/

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

[2] 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

[3] Bartsch T., Weth T., Three nodal solutions of singularly perturbed elliptic equations on domains without topology, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (3) (2005) 259-281. | Numdam | MR 2136244 | Zbl 1114.35068

[4] 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

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

[6] Cerami G., Molle R., Multiple positive solutions for singularly perturbed elliptic problems in exterior domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (5) (2003) 759-777. | Numdam | MR 1995501 | Zbl pre01975933

[7] Cerami G., Passaseo D., Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology, Nonlinear Anal. 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 Anal. 24 (11) (1995) 1533-1547. | MR 1328581 | Zbl 0845.35026

[9] Cerami G., Passaseo D., The effect of concentrating potentials in some singularly perturbed problems, Calc. Var. Partial Differential Equations 17 (3) (2003) 257-281. | MR 1989833 | Zbl pre01969061

[10] Coffman C.V., Marcus M., Existence theorems for superlinear elliptic Dirichlet problems in exterior domains, in: Nonlinear Functional Analysis and its Applications, Part 1, Berkeley, CA, 1983, Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 271-282. | MR 843566 | Zbl 0596.35048

[11] Cornea O., Lupton G., Oprea J., Tanré D., Lusternik Schnirelmann Category, American Mathematical Society, Providence, 2003. | MR 1990857 | Zbl 1032.55001

[12] Esteban M.J., Nonlinear elliptic problems in strip-like domains: symmetry of positive vortex rings, Nonlinear Anal. 7 (4) (1983) 365-379. | MR 696736 | Zbl 0513.35035

[13] Esteban M.J., Lions P.L., Existence and nonexistence results for semilinear elliptic problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A 93 (1/2) (1982/83) 1-14. | MR 688279 | Zbl 0506.35035

[14] Fadell E., Husseini S., Relative category, products and coproducts, Rend. Sem. Mat. Fis. Milano 64 (1994) 99-115. | MR 1397466 | Zbl 0860.55011

[15] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in R N , in: Mathematical Analysis and Applications - Part A, Adv. Math. Supplementary Stud., vol. 7-A, Academic Press, 1981, pp. 369-402. | Zbl 0469.35052

[16] Kwong M.K., Uniqueness of positive solutions of Δu-u+u p =0, Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032

[17] J. Molina, R. Molle, Multiplicity of positive solutions for elliptic problems in domains with unbounded boundary, Proc. Edinburgh Math. Soc., in press.

[18] Molle R., Semilinear elliptic problems in unbounded domains with unbounded boundary, Asymptotic Anal. 38 (3/4) (2004) 293-307. | MR 2072061 | Zbl 1080.35024

[19] 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

[20] Schwartz J.T., Nonlinear Functional Analysis, Notes on Math. Appl., Gordon and Breach Science Publishers, New York, 1969. | MR 433481 | Zbl 0203.14501

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

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

[23] H.C. Wang, Palais-Smale approaches to semilinear elliptic equations in unbounded domains, Electron. J. Differential Equations, Monograph 06, 2004. | Zbl 1115.35036

[24] Willem M., Minimax Theorems, Progr. Nonlinear Differential Equations Appl., vol. 24, Birkhäuser Boston, Inc., Boston, MA, 1996. | MR 1400007 | Zbl 0856.49001