Solutions of an elliptic system with a nearly critical exponent
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 1, page 181-200
- ISSN: 0294-1449
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topGuerra, I. A.. "Solutions of an elliptic system with a nearly critical exponent." Annales de l'I.H.P. Analyse non linéaire 25.1 (2008): 181-200. <http://eudml.org/doc/78780>.
@article{Guerra2008,
author = {Guerra, I. A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {semilinear elliptic system; asymptotic behavior; critical exponent},
language = {eng},
number = {1},
pages = {181-200},
publisher = {Elsevier},
title = {Solutions of an elliptic system with a nearly critical exponent},
url = {http://eudml.org/doc/78780},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Guerra, I. A.
TI - Solutions of an elliptic system with a nearly critical exponent
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 1
SP - 181
EP - 200
LA - eng
KW - semilinear elliptic system; asymptotic behavior; critical exponent
UR - http://eudml.org/doc/78780
ER -
References
top- [1] Atkinson F.V., Peletier L.A., Elliptic equations with nearly critical growth, J. Differential Equations70 (1987) 349-365. Zbl0657.35058MR915493
- [2] M. Ben Ayed, K. El Mehdi, On a biharmonic equation involving nearly critical exponent, preprint. Zbl1162.35375MR2314331
- [3] Brézis H., Peletier L.A., Asymptotics for elliptic equations involving critical growth, in: Partial Differential Equations and the Calculus of Variations, vol. I, Birkhäuser, Boston, MA, 1989, pp. 149-192. Zbl0685.35013MR1034005
- [4] Clément Ph., de Figueiredo D.G., Mitidieri E., Positive solutions of semilinear elliptic systems, Comm. Partial Differential Equations17 (1992) 923-940. Zbl0818.35027MR1177298
- [5] Chen X., Li C., Ou B., Classification of solutions for a system of integral equations, Comm. Partial Differential Equations30 (2005) 59-65. Zbl1073.45005MR2131045
- [6] Chou K.-S., Geng D., Asymptotics of positive solutions for a biharmonic equation involving critical exponent, Differential Integral Equations13 (7–9) (2000) 921-940. Zbl0977.35043MR1775240
- [7] De Figueiredo D.G., Felmer P., On superquadratic elliptic systems, Trans. Amer. Math. Soc.343 (1994) 99-116. Zbl0799.35063MR1214781
- [8] De Figueiredo D.G., Lions P.L., Nussbaum R.D., A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures Appl.61 (1982) 41-63. Zbl0452.35030MR664341
- [9] De Figueiredo D.G., Ruf B., Elliptic systems with nonlinearities of arbitrary growth, Mediterranean. J. Math.1 (4) (2004) 417-431. Zbl1135.35026MR2112747
- [10] Flucher M., Wei J., Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots, Manuscripta Mat.94 (1997) 337-346. Zbl0892.35061MR1485441
- [11] Gidas B., Ni W., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979) 209-243. Zbl0425.35020MR544879
- [12] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
- [13] Guerra I.A., Asymptotic behaviors of a semilinear elliptic system with a large exponent, J. Dynam. Differential Equations19 (1) (2007) 243-263. Zbl1186.35015MR2279954
- [14] Hammami M., Concentration phenomena for fourth-order elliptic equations with critical exponent, Electron. J. Differential Equations121 (2004) 22. Zbl1129.35416MR2108892
- [15] Han Z.-C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré8 (2) (1991) 159-174. Zbl0729.35014MR1096602
- [16] Hulshof J., van der Vorst R.C.A.M., Differential systems with strongly indefinite variational structure, J. Funct. Anal.114 (1993) 32-58. Zbl0793.35038MR1220982
- [17] Hulshof J., van der Vorst R.C.A.M., Asymptotic behaviour of ground states, Proc. Amer. Math. Soc.124 (8) (1996) 2423-2431. Zbl0860.35029MR1363170
- [18] Lieb E.H., Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities, Ann. of Math.118 (1983) 349-374. Zbl0527.42011MR717827
- [19] Mitidieri E., A Rellich type identity and applications, Comm. Partial Differential Equations18 (1–2) (1993) 125-151. Zbl0816.35027MR1211727
- [20] Peletier L.A., van der Vorst R.C.A.M., Existence and nonexistence of positive solutions of non-linear elliptic systems and the biharmonic equation, Differential Integral Equations5 (4) (1992) 747-767. Zbl0758.35029MR1167492
- [21] Rey O., Proof of two conjectures of H. Brézis and L.A. Peletier, Manuscripta Mat.65 (1) (1989) 19-37. Zbl0708.35032MR1006624
- [22] Struwe M., Global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z.187 (1984) 511-517. Zbl0535.35025MR760051
- [23] van der Vorst R.C.A.M., Variational identities and applications to differential systems, Arch. Ration. Mech. Anal.116 (1991) 375-398. Zbl0796.35059MR1132768
- [24] Wang X.J., Sharp constant in a Sobolev inequality, Nonlinear Anal. TMA20 (1993) 261-268. Zbl0803.35045MR1202203
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