Solutions of an elliptic system with a nearly critical exponent
Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 1, p. 181-200
@article{AIHPC_2008__25_1_181_0,
     author = {Guerra, I. A.},
     title = {Solutions of an elliptic system with a nearly critical exponent},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {25},
     number = {1},
     year = {2008},
     pages = {181-200},
     doi = {10.1016/j.anihpc.2006.11.008},
     zbl = {1136.35025},
     mrnumber = {2383086},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2008__25_1_181_0}
}
Guerra, I. A. Solutions of an elliptic system with a nearly critical exponent. Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 1, pp. 181-200. doi : 10.1016/j.anihpc.2006.11.008. http://www.numdam.org/item/AIHPC_2008__25_1_181_0/

[1] Atkinson F.V., Peletier L.A., Elliptic equations with nearly critical growth, J. Differential Equations 70 (1987) 349-365. | MR 915493 | Zbl 0657.35058

[2] M. Ben Ayed, K. El Mehdi, On a biharmonic equation involving nearly critical exponent, preprint. | MR 2314331 | Zbl 1162.35375

[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. | MR 1034005 | Zbl 0685.35013

[4] Clément Ph., De Figueiredo D.G., Mitidieri E., Positive solutions of semilinear elliptic systems, Comm. Partial Differential Equations 17 (1992) 923-940. | MR 1177298 | Zbl 0818.35027

[5] Chen X., Li C., Ou B., Classification of solutions for a system of integral equations, Comm. Partial Differential Equations 30 (2005) 59-65. | MR 2131045 | Zbl 1073.45005

[6] Chou K.-S., Geng D., Asymptotics of positive solutions for a biharmonic equation involving critical exponent, Differential Integral Equations 13 (7-9) (2000) 921-940. | MR 1775240 | Zbl 0977.35043

[7] De Figueiredo D.G., Felmer P., On superquadratic elliptic systems, Trans. Amer. Math. Soc. 343 (1994) 99-116. | MR 1214781 | Zbl 0799.35063

[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. | MR 664341 | Zbl 0452.35030

[9] De Figueiredo D.G., Ruf B., Elliptic systems with nonlinearities of arbitrary growth, Mediterranean. J. Math. 1 (4) (2004) 417-431. | MR 2112747 | Zbl 1135.35026

[10] Flucher M., Wei J., Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots, Manuscripta Mat. 94 (1997) 337-346. | MR 1485441 | Zbl 0892.35061

[11] Gidas B., Ni W., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR 544879 | Zbl 0425.35020

[12] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., Springer-Verlag, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[13] Guerra I.A., Asymptotic behaviors of a semilinear elliptic system with a large exponent, J. Dynam. Differential Equations 19 (1) (2007) 243-263. | MR 2279954 | Zbl pre05166186

[14] Hammami M., Concentration phenomena for fourth-order elliptic equations with critical exponent, Electron. J. Differential Equations 121 (2004) 22. | MR 2108892 | Zbl 1129.35416

[15] Han Z.-C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré 8 (2) (1991) 159-174. | Numdam | MR 1096602 | Zbl 0729.35014

[16] Hulshof J., Van Der Vorst R.C.A.M., Differential systems with strongly indefinite variational structure, J. Funct. Anal. 114 (1993) 32-58. | MR 1220982 | Zbl 0793.35038

[17] Hulshof J., Van Der Vorst R.C.A.M., Asymptotic behaviour of ground states, Proc. Amer. Math. Soc. 124 (8) (1996) 2423-2431. | MR 1363170 | Zbl 0860.35029

[18] Lieb E.H., Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. 118 (1983) 349-374. | MR 717827 | Zbl 0527.42011

[19] Mitidieri E., A Rellich type identity and applications, Comm. Partial Differential Equations 18 (1-2) (1993) 125-151. | MR 1211727 | Zbl 0816.35027

[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 Equations 5 (4) (1992) 747-767. | MR 1167492 | Zbl 0758.35029

[21] Rey O., Proof of two conjectures of H. Brézis and L.A. Peletier, Manuscripta Mat. 65 (1) (1989) 19-37. | MR 1006624 | Zbl 0708.35032

[22] Struwe M., Global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187 (1984) 511-517. | MR 760051 | Zbl 0535.35025

[23] Van Der Vorst R.C.A.M., Variational identities and applications to differential systems, Arch. Ration. Mech. Anal. 116 (1991) 375-398. | MR 1132768 | Zbl 0796.35059

[24] Wang X.J., Sharp constant in a Sobolev inequality, Nonlinear Anal. TMA 20 (1993) 261-268. | MR 1202203 | Zbl 0803.35045