Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary
Giovanna Cerami; Riccardo Molle; Donato Passaseo
Annales de l'I.H.P. Analyse non linéaire (2007)
- Volume: 24, Issue: 1, page 41-60
- ISSN: 0294-1449
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topCerami, Giovanna, Molle, Riccardo, and Passaseo, Donato. "Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary." Annales de l'I.H.P. Analyse non linéaire 24.1 (2007): 41-60. <http://eudml.org/doc/78728>.
@article{Cerami2007,
author = {Cerami, Giovanna, Molle, Riccardo, Passaseo, Donato},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear elliptic problems; unbounded domains; unbounded boundary},
language = {eng},
number = {1},
pages = {41-60},
publisher = {Elsevier},
title = {Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary},
url = {http://eudml.org/doc/78728},
volume = {24},
year = {2007},
}
TY - JOUR
AU - Cerami, Giovanna
AU - Molle, Riccardo
AU - Passaseo, Donato
TI - Positive solutions of semilinear elliptic problems in unbounded domains with unbounded boundary
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 1
SP - 41
EP - 60
LA - eng
KW - nonlinear elliptic problems; unbounded domains; unbounded boundary
UR - http://eudml.org/doc/78728
ER -
References
top- [1] Bahri A., Li Y.Y., On a min–max procedure for the existence of a positive solution for certain scalar field equations in , Rev. Mat. Iberoamericana6 (1/2) (1990) 1-15. Zbl0731.35036
- [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 Linéaire14 (3) (1997) 365-413. Zbl0883.35045MR1450954
- [3] Bartsch T., Weth T., Three nodal solutions of singularly perturbed elliptic equations on domains without topology, Ann. Inst. H. Poincaré Anal. Non Linéaire22 (3) (2005) 259-281. Zbl1114.35068MR2136244
- [4] Benci V., Cerami G., Positive solutions of some nonlinear elliptic problems in exterior domains, Arch. Rational Mech. Anal.99 (1987) 283-300. Zbl0635.35036MR898712
- [5] Berestycki H., Lions P.L., Nonlinear scalar fields equations – I. Existence of a ground-state, Arch. Rational Mech. Anal.82 (1983) 313-346. Zbl0533.35029
- [6] Cerami G., Molle R., Multiple positive solutions for singularly perturbed elliptic problems in exterior domains, Ann. Inst. H. Poincaré Anal. Non Linéaire20 (5) (2003) 759-777. Zbl1274.35080MR1995501
- [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. Zbl0810.35024
- [8] Cerami G., Passaseo D., Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains, Nonlinear Anal.24 (11) (1995) 1533-1547. Zbl0845.35026MR1328581
- [9] Cerami G., Passaseo D., The effect of concentrating potentials in some singularly perturbed problems, Calc. Var. Partial Differential Equations17 (3) (2003) 257-281. Zbl1290.35050MR1989833
- [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. Zbl0596.35048MR843566
- [11] Cornea O., Lupton G., Oprea J., Tanré D., Lusternik Schnirelmann Category, American Mathematical Society, Providence, 2003. Zbl1032.55001MR1990857
- [12] Esteban M.J., Nonlinear elliptic problems in strip-like domains: symmetry of positive vortex rings, Nonlinear Anal.7 (4) (1983) 365-379. Zbl0513.35035MR696736
- [13] Esteban M.J., Lions P.L., Existence and nonexistence results for semilinear elliptic problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A93 (1/2) (1982/83) 1-14. Zbl0506.35035MR688279
- [14] Fadell E., Husseini S., Relative category, products and coproducts, Rend. Sem. Mat. Fis. Milano64 (1994) 99-115. Zbl0860.55011MR1397466
- [15] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in , in: Mathematical Analysis and Applications – Part A, Adv. Math. Supplementary Stud., vol. 7-A, Academic Press, 1981, pp. 369-402. Zbl0469.35052
- [16] Kwong M.K., Uniqueness of positive solutions of , Arch. Rational Mech. Anal.105 (1989) 243-266. Zbl0676.35032MR969899
- [17] J. Molina, R. Molle, Multiplicity of positive solutions for elliptic problems in domains with unbounded boundary, Proc. Edinburgh Math. Soc., in press. Zbl1160.35411
- [18] Molle R., Semilinear elliptic problems in unbounded domains with unbounded boundary, Asymptotic Anal.38 (3/4) (2004) 293-307. Zbl1080.35024MR2072061
- [19] Molle R., Passaseo D., Multiple solutions of nonlinear elliptic Dirichlet problems in exterior domains, Nonlinear Anal. Ser. A: Theory & Methods39 (4) (2000) 447-462. Zbl0939.35071MR1725399
- [20] Schwartz J.T., Nonlinear Functional Analysis, Notes on Math. Appl., Gordon and Breach Science Publishers, New York, 1969. Zbl0203.14501MR433481
- [21] Strauss W.A., Existence of solitary waves in higher dimensions, Comm. Math. Phys.55 (1977) 149-162. Zbl0356.35028MR454365
- [22] Struwe M., Variational Methods – Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 1990. Zbl0746.49010
- [23] H.C. Wang, Palais–Smale approaches to semilinear elliptic equations in unbounded domains, Electron. J. Differential Equations, Monograph 06, 2004. Zbl1115.35036
- [24] Willem M., Minimax Theorems, Progr. Nonlinear Differential Equations Appl., vol. 24, Birkhäuser Boston, Inc., Boston, MA, 1996. Zbl0856.49001MR1400007
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