Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, part II
Gazzola, Filippo ; Peletier, Bert ; Pucci, Patrizia ; Serrin, James
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 947-974 / Harvested from Numdam
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@article{AIHPC_2003__20_6_947_0,
     author = {Gazzola, Filippo and Peletier, Bert and Pucci, Patrizia and Serrin, James},
     title = {Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, part II},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {947-974},
     doi = {10.1016/S0294-1449(03)00013-1},
     mrnumber = {2008685},
     zbl = {1086.35041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_6_947_0}
}

Gazzola, Filippo; Peletier, Bert; Pucci, Patrizia; Serrin, James. Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, part II. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 947-974. doi : 10.1016/S0294-1449(03)00013-1. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_6_947_0/

[1] Abramowitz M., Stegun I.A., Handbook of Mathematical Functions, Dover, 1972.

[2] Atkinson F.V., Peletier L.A., Ground states of −Δu=f(u) and the Emden-Fowler equation, Arch. Rational Mech. Anal. 93 (1986) 103-127. | Zbl 0606.35029

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

[4] Berestycki H., Lions P.L., Nonlinear scalar field equations, I, Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983) 313-345. | MR 695535 | Zbl 0533.35029

[5] Brezis H., Peletier L.A., Asymptotics for elliptic equations involving critical exponents, in: Partial Differential Equations and Calculus of Variations, Birkhäuser, 1989, pp. 149-192. | MR 1034005 | Zbl 0685.35013

[6] Franchi B., Lanconelli E., Serrin J., Existence and uniqueness of nonnegative solutions of quasilinear equations in Rn, Adv. Math. 118 (1996) 177-243. | MR 1378680 | Zbl 0853.35035

[7] García Azorero J.P., Peral Alonso I., On limits of solutions of elliptic problems with nearly critical exponent, Comm. Part. Differential Equations 17 (1992) 2113-2126. | MR 1194752 | Zbl 0799.35066

[8] Gazzola F., Critical growth quasilinear elliptic problems with shifting subcritical perturbation, Differential Integral Equations 14 (2001) 513-528. | MR 1824741 | Zbl 1030.35076

[9] Gazzola F., Serrin J., Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, Ann. Inst. H. Poincaré AN 19 (2002) 477-504. | Numdam | MR 1912264 | Zbl 1013.35031

[10] Gazzola F., Serrin J., Tang M., Existence of ground states and free boundary problems for quasilinear elliptic operators, Adv. Differential Equations 5 (2000) 1-30. | MR 1734535 | Zbl 0987.35064

[11] Knaap M.C., Peletier L.A., Quasilinear elliptic equations with nearly critical growth, Comm. Part. Differential Equations 14 (1989) 1351-1383. | MR 1022990 | Zbl 0696.35052

[12] Ni W.M., Serrin J., Nonexistence theorems for quasilinear partial differential equations, Rend. Circolo Mat. Palermo (Centenary Supplement) Ser. II 8 (1985) 171-185. | MR 881397 | Zbl 0625.35028

[13] Ni W.M., Serrin J., Existence and nonexistence theorems for ground states of quasilinear partial differential equations. The anomalous case, Accad. Naz. dei Lincei Atti dei Convegni 77 (1986) 231-257.

[14] Pucci P., Serrin J., A general variational identity, Indiana Univ. Math. J. 35 (1986) 681-703. | MR 855181 | Zbl 0625.35027

[15] Pucci P., Serrin J., Uniqueness of ground states for quasilinear elliptic operators, Indiana Univ. Math. J. 47 (1998) 501-528. | MR 1647924 | Zbl 0920.35054

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

[17] Rey O., The role of Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990) 1-52. | MR 1040954 | Zbl 0786.35059

[18] Serrin J., Tang M., Uniqueness of ground states for quasilinear elliptic equations, Indiana Univ. Math. J. 49 (2000) 897-923. | MR 1803216 | Zbl 0979.35049