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.
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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},
pages = {41--60},
publisher = {Elsevier},
volume = {24},
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year = {2007},
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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://archive.numdam.org/articles/10.1016/j.anihpc.2005.09.007/

[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

[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 | Zbl

[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 | Zbl

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

[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

[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

[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

[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 | Zbl

[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

[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 | Zbl

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

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

[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 | Zbl

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

[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

[16] Kwong M.K., Uniqueness of positive solutions of $\Delta u-u+{u}^{p}=0$, Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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