Multiple solutions of supercritical elliptic problems in perturbed domains

Riccardo Molle; Donato Passaseo

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 3, page 389-405
  • ISSN: 0294-1449

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Molle, Riccardo, and Passaseo, Donato. "Multiple solutions of supercritical elliptic problems in perturbed domains." Annales de l'I.H.P. Analyse non linéaire 23.3 (2006): 389-405. <http://eudml.org/doc/78696>.

@article{Molle2006,
author = {Molle, Riccardo, Passaseo, Donato},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {supercritical problems; changing sign solutions; multiplicity of solutions; number of nodal regions},
language = {eng},
number = {3},
pages = {389-405},
publisher = {Elsevier},
title = {Multiple solutions of supercritical elliptic problems in perturbed domains},
url = {http://eudml.org/doc/78696},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Molle, Riccardo
AU - Passaseo, Donato
TI - Multiple solutions of supercritical elliptic problems in perturbed domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 3
SP - 389
EP - 405
LA - eng
KW - supercritical problems; changing sign solutions; multiplicity of solutions; number of nodal regions
UR - http://eudml.org/doc/78696
ER -

References

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  7. [7] Ding W.Y., Positive solutions of Δ u + u ( n + 2 ) / ( n - 2 ) = 0 on contractible domains, J. Partial Differential Equations2 (4) (1989) 83-88. Zbl0694.35067MR1027983
  8. [8] Kazdan J., Warner F.W., Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math.28 (5) (1975) 567-597. Zbl0325.35038MR477445
  9. [9] Krasnosel'skii M.A., Topological Methods in the Theory of Nonlinear Integral Equations, A Pergamon Press Book, The Macmillan Co., New York, 1964, (Translation edited by J. Burlak). Zbl0111.30303MR159197
  10. [10] Molle R., Passaseo D., Positive solutions for slightly super-critical elliptic equations in contractible domains, Preprint Dip. Matem. Univ. Lecce, n. 6, 2001 and, C. R. Acad. Sci. Paris Sér. I Math.335 (5) (2002) 459-462. Zbl1010.35043MR1937113
  11. [11] Molle R., Passaseo D., Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains, C. R. Acad. Sci. Paris Sér. I Math.335 (12) (2002) 1029-1032. Zbl1032.35071MR1955582
  12. [12] Molle R., Passaseo D., Positive solutions of slightly supercritical elliptic equations in symmetric domains, Ann. Inst. H. Poincaré Anal. Non Linéaire21 (5) (2004) 639-656. Zbl1149.35353MR2086752
  13. [13] Molle R., Passaseo D., On the existence of positive solutions of slightly supercritical elliptic equations, Adv. Nonlinear Stud.3 (3) (2003) 301-326. Zbl1094.35051MR1989741
  14. [14] R. Molle, D. Passaseo, Nonlinear elliptic equations with large supercritical exponents, Preprint Dip. Mat. Università di Roma “Tor Vergata”, 2003; Calc. Var. Partial Differential Equations, submitted for publication. Zbl1093.35022
  15. [15] R. Molle, D. Passaseo, in preparation. 
  16. [16] Passaseo D., Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math.65 (2) (1989) 147-165. Zbl0701.35068MR1011429
  17. [17] Passaseo D., Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal.114 (1) (1993) 97-105. Zbl0793.35039MR1220984
  18. [18] Passaseo D., The effect of the domain shape on the existence of positive solutions of the equation Δ u + u 2 * - 1 = 0 , Topol. Methods Nonlinear Anal.3 (1) (1994) 27-54. Zbl0812.35032MR1272886
  19. [19] Passaseo D., New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations8 (3) (1995) 577-586. Zbl0821.35056MR1306576
  20. [20] Passaseo D., Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J.92 (2) (1998) 429-457. Zbl0943.35034MR1612734
  21. [21] Pohožaev S.I., On the eigenfunctions of the equation Δ u + λ f u = 0 , Soviet Math. Dokl.6 (1965) 1408-1411. Zbl0141.30202MR192184

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