Positive solutions of slightly supercritical elliptic equations in symmetric domains
Riccardo Molle; Donato Passaseo
Annales de l'I.H.P. Analyse non linéaire (2004)
- Volume: 21, Issue: 5, page 639-656
- ISSN: 0294-1449
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topMolle, Riccardo, and Passaseo, Donato. "Positive solutions of slightly supercritical elliptic equations in symmetric domains." Annales de l'I.H.P. Analyse non linéaire 21.5 (2004): 639-656. <http://eudml.org/doc/78632>.
@article{Molle2004,
author = {Molle, Riccardo, Passaseo, Donato},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Supercritical problems; Multi-spike solutions; Contractible domains},
language = {eng},
number = {5},
pages = {639-656},
publisher = {Elsevier},
title = {Positive solutions of slightly supercritical elliptic equations in symmetric domains},
url = {http://eudml.org/doc/78632},
volume = {21},
year = {2004},
}
TY - JOUR
AU - Molle, Riccardo
AU - Passaseo, Donato
TI - Positive solutions of slightly supercritical elliptic equations in symmetric domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 5
SP - 639
EP - 656
LA - eng
KW - Supercritical problems; Multi-spike solutions; Contractible domains
UR - http://eudml.org/doc/78632
ER -
References
top- [1] Atkinson F.V., Peletier L.A., Elliptic equations with nearly critical growth, J. Differential Equations70 (3) (1987) 349-365. Zbl0657.35058MR915493
- [2] Bahri A., Coron J.M., On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math.41 (1988) 253-294. Zbl0649.35033MR929280
- [3] Bahri A., Li Y.Y., Rey O., On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var.3 (1) (1995) 67-93. Zbl0814.35032MR1384837
- [4] Brezis H., Elliptic equations with limiting Sobolev exponents – The impact of topology, Comm. Pure Appl. Math.39 (S suppl.) (1986) S17-S39. Zbl0601.35043MR861481
- [5] Brezis H., Peletier L.A., Asymptotics for elliptic equations involving critical growth, in: Colombini, Modica, Spagnolo (Eds.), P.D.E. and the Calculus of Variations, Birkhäuser, Basel, 1989, pp. 149-192. Zbl0685.35013MR1034005
- [6] Coron J.M., Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I Math.299 (7) (1984) 209-212. Zbl0569.35032MR762722
- [7] Dancer E.N., A note on an equation with critical exponent, Bull. London Math. Soc.20 (6) (1988) 600-602. Zbl0646.35027MR980763
- [8] Dancer E.N., Zhang K., Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains, Nonlinear Anal. Ser. A: TMA41 (5/6) (2000) 745-761. Zbl0960.35035MR1780642
- [9] Del Pino M., Felmer P., Musso M., Multipeak solutions for super-critical elliptic problems in domains with small holes, J. Differential Equations182 (2) (2002) 511-540. Zbl1014.35028MR1900333
- [10] Ding W.Y., Positive solutions of Δu+u(n+2)/(n−2)=0 on contractible domains, J. Partial Differential Equations2 (4) (1989) 83-88. Zbl0694.35067
- [11] Han Z.C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire8 (2) (1991) 159-174. Zbl0729.35014MR1096602
- [12] Kazdan J., Warner F.W., Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math.28 (5) (1975) 567-597. Zbl0325.35038MR477445
- [13] Molle R., Passaseo D., Positive solutions for slightly super-critical elliptic equations in contractible domains, Preprint Dip. Matem. Univ. Lecce6 (2001), C. R. Acad. Sci. Paris Sér. I Math.335 (5) (2002) 459-462. Zbl1010.35043MR1937113
- [14] 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
- [15] R. Molle, D. Passaseo, On the existence of positive solutions of slightly supercritical elliptic equations, preprint. Zbl1094.35051MR1989741
- [16] R. Molle, D. Passaseo, A finite dimensional reduction method for slightly supercritical elliptic problems, preprint. Zbl1133.35360MR2096946
- [17] 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
- [18] Passaseo D., Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal.114 (1) (1993) 97-105. Zbl0793.35039MR1220984
- [19] Passaseo D., New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations8 (3) (1995) 577-586. Zbl0821.35056MR1306576
- [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] Pohožaev S.I., On the eigenfunctions of the equation Δu+λf(u)=0, Soviet. Math. Dokl.6 (1965) 1408-1411.
- [22] Rey O., Sur un problème variationnel non compact: l'effet de petits trous dans le domaine, C. R. Acad. Sci. Paris Sér. I Math.308 (12) (1989) 349-352. Zbl0686.35047MR992090
- [23] Rey O., A multiplicity result for a variational problem with lack of compactness, Nonlinear Anal.13 (10) (1989) 1241-1249. Zbl0702.35101MR1020729
- [24] Rey O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal.89 (1) (1990) 1-52. Zbl0786.35059MR1040954
- [25] Rey O., The topological impact of critical points at infinity in a variational problem with lack of compactness: the dimension 3, Adv. Differential Equations4 (4) (1999) 581-616. Zbl0952.35051MR1693274
- [26] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl.110 (1976) 353-372. Zbl0353.46018MR463908
- [27] Yan S., High-energy solutions for a nonlinear elliptic problem with slightly supercritical exponent, Nonlinear Anal. Ser. A: Theory Methods38 (4) (1999) 527-546. Zbl0956.35043MR1707876
Citations in EuDML Documents
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