Multiple positive solutions for singularly perturbed elliptic problems in exterior domains

Giovanna Cerami; Riccardo Molle

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 5, page 759-777
  • ISSN: 0294-1449

How to cite

top

Cerami, Giovanna, and Molle, Riccardo. "Multiple positive solutions for singularly perturbed elliptic problems in exterior domains." Annales de l'I.H.P. Analyse non linéaire 20.5 (2003): 759-777. <http://eudml.org/doc/78596>.

@article{Cerami2003,
author = {Cerami, Giovanna, Molle, Riccardo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {exterior domains; lack of compactness; multiplicity of solutions},
language = {eng},
number = {5},
pages = {759-777},
publisher = {Elsevier},
title = {Multiple positive solutions for singularly perturbed elliptic problems in exterior domains},
url = {http://eudml.org/doc/78596},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Cerami, Giovanna
AU - Molle, Riccardo
TI - Multiple positive solutions for singularly perturbed elliptic problems in exterior domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 5
SP - 759
EP - 777
LA - eng
KW - exterior domains; lack of compactness; multiplicity of solutions
UR - http://eudml.org/doc/78596
ER -

References

top
  1. [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 Linéaire14 (3) (1997) 365-413. Zbl0883.35045MR1450954
  2. [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. Iberoamericana6 (1–2) (1990) 1-15. Zbl0731.35036MR1086148
  3. [3] Benci V., Cerami G., Positive solutions of some nonlinear elliptic problems in exterior domains, Arch. Rational Mech. Anal.99 (1987) 283-300. Zbl0635.35036MR898712
  4. [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. Zbl0705.35042
  5. [5] Berestycki H., Lions P.L., Nonlinear scalar fields equations – I. Existence of a ground-state, Arch. Rational Mech. Anal.82 (1983) 313-346. Zbl0533.35029MR695535
  6. [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. Zbl1094.35501
  7. [7] Cerami G., Passaseo D., Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology, Nonlinear Analysis TMA18 (2) (1992) 109-119. Zbl0810.35024
  8. [8] Cerami G., Passaseo D., Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains, Nonlinear Analysis TMA24 (11) (1995) 1533-1547. Zbl0845.35026MR1328581
  9. [9] G. Cerami, D. Passaseo, Effect of concentrating potentials in some singularly perturbed problems, Calculus of Variations and PDE, to appear. Zbl1290.35050MR1989833
  10. [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. Zbl0469.35052MR634248
  11. [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. Zbl0863.35035MR1326704
  12. [12] Kwong M.K., Uniqueness of positive solutions of Δu−u+up=0, Arch. Rational Mech. Anal.105 (1989) 243-266. Zbl0676.35032
  13. [13] Molle R., Musso M., Passaseo D., Positive solutions for a class of nonlinear elliptic problems in RN, Proc. Roy. Soc. Edinburgh Sect. A130 (1) (2000) 141-166. Zbl0947.35062MR1742584
  14. [14] Molle R., Passaseo D., On the behaviour of the solutions for a class of nonlinear elliptic problems in exterior domains, Discrete Contin. Dynam. Systems4 (3) (1998) 445-454. Zbl0951.35052MR1612740
  15. [15] 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
  16. [16] Strauss W.A., Existence of solitary waves in higher dimensions, Comm. Math. Phys.55 (1977) 149-162. Zbl0356.35028MR454365
  17. [17] Struwe M., Variational Methods – Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 1990. Zbl0746.49010MR1078018

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.