Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler equation
Wei, Juncheng ; Ye, Dong ; Zhou, Feng
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 425-447 / Harvested from Numdam
@article{AIHPC_2008__25_3_425_0,
     author = {Wei, Juncheng and Ye, Dong and Zhou, Feng},
     title = {Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {425-447},
     doi = {10.1016/j.anihpc.2007.02.001},
     mrnumber = {2422074},
     zbl = {1155.35037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_3_425_0}
}
Wei, Juncheng; Ye, Dong; Zhou, Feng. Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler equation. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 425-447. doi : 10.1016/j.anihpc.2007.02.001. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_3_425_0/

[1] Bandle C., Flucher M., Harmonic radius and concentration of energy hyperbolic radius and Liouville’s equations ΔU=e U and ΔU=U (n+2)/(n-2) , SIAM Rev. 38 (2) (1996) 191-238. | MR 1391227 | Zbl 0857.35034

[2] Baraket S., Pacard F., Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations 6 (1) (1998) 1-38. | MR 1488492 | Zbl 0890.35047

[3] Brezis H., Merle F., Uniform estimates and blow-up behavior for solutions of -Δu=Vxe u in two dimensions, Comm. Partial Differential Equations 16 (8-9) (1991) 1223-1253. | MR 1132783 | Zbl 0746.35006

[4] Caglioti E., Lions P.L., Marchioro C., Pulvirenti M., A special class of stationary flows for two-dimensional Euler-equations: a statistical mechanics description, Comm. Math. Phys. 143 (1992) 501-525. | MR 1145596 | Zbl 0745.76001

[5] Caglioti E., Lions P.L., Marchioro C., Pulvirenti M., A special class of stationary flows for two-dimensional Euler-equations: a statistical mechanics description, Part II, Comm. Math. Phys. 174 (1995) 229-260. | MR 1362165 | Zbl 0840.76002

[6] Chandrasekhar S., An Introduction to the Study of Stellar Structure, Dover, New York, 1957. | MR 92663 | Zbl 0079.23901

[7] Chanillo S., Kiessling M., Surfaces with prescribed Gauss curvature, Duke Math. J. 105 (2) (2000) 309-353. | MR 1793614 | Zbl 1023.53005

[8] Chen W., Li C., Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991) 615-623. | MR 1121147 | Zbl 0768.35025

[9] Del Pino M., Kowalczyk M., Musso M., Singular limits in Liouville-type equations, Calc. Var. Partial Differential Equations 24 (2005) 47-81. | MR 2157850 | Zbl 1088.35067

[10] Esposito P., Grossi M., Pistoia A., On the existence of blowing-up solutions for a mean field equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) 227-257. | Numdam | MR 2124164 | Zbl 1129.35376

[11] Gelfand I.M., Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl. 29 (1963) 295-381. | MR 153960 | Zbl 0127.04901

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

[13] Joseph D.D., Lundgren T.S., Quasilinear problems driven by positive sources, Arch. Rat. Mech. Anal. 49 (1973) 241-269. | MR 340701 | Zbl 0266.34021

[14] Li Y.Y., Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999) 421-444. | MR 1673972 | Zbl 0928.35057

[15] Li Y.Y., Shafrir I., Blow-up analysis for solutions of -Δu=Ve u in dimension two, Indiana Univ. Math. J. 43 (4) (1994) 1255-1270. | MR 1322618 | Zbl 0842.35011

[16] Lin S.S., Positive radial solutions and non-radial bifurcation for semilinear elliptic equations in annular domains, J. Differential Eqnuations 86 (1990) 367-391. | MR 1064016 | Zbl 0734.35073

[17] Lin C.S., Topological degree for mean field equations on S 2 , Duke Math. J. 104 (3) (2000) 501-536. | MR 1781481 | Zbl 0964.35038

[18] Ma L., Wei J., Convergence for a Liouville equation, Comm. Math. Helv. 76 (2001) 506-514. | MR 1854696 | Zbl 0987.35056

[19] Mignot F., Murat F., Puel J.P., Variation d'un point retournement par rapport au domaine, Comm. Partial Differential Equations 4 (1979) 1263-1297. | MR 546644 | Zbl 0422.35039

[20] Mizoguchi N., Suzuki T., Equations of gas combustion: S-shaped bifurcation and mushrooms, J. Differential Equations 134 (1997) 183-215. | MR 1432094 | Zbl 0876.35037

[21] Nagasaki K., Suzuki T., Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearities, Asymptotic Anal. 3 (1990) 173-188. | MR 1061665 | Zbl 0726.35011

[22] Nagasaki K., Suzuki T., Radial solutions for Δu+λe u =0 on annuli in higher dimensions, J. Differential Equations 100 (1992) 137-161. | MR 1187866 | Zbl 0776.35047

[23] Pacard F., Radial and non-radial solutions of -Δu=λfu on an annulus of R n , n3, J. Differential Equations 101 (1993) 103-138. | MR 1199485 | Zbl 0799.35089

[24] Pohozaev S.I., Eigenfunctions of the equation Δu+λfu=0, Soviet Math. Dokl. 6 (1965) 1408-1411. | MR 192184 | Zbl 0141.30202

[25] Senba T., Suzuki T., Some structures of the solution set from stationary system of chemotaxis, Adv. Math. Sci. Appl. 10 (2000) 191-224. | MR 1769174 | Zbl 0999.35031

[26] Wei J., Ye D., Zhou F., Bubbling solutions for an anisotropic Emden-Fowler equation, Calc. Var. Partial Differential Equations 28 (2007) 217-247. | MR 2284567 | Zbl 1159.35402

[27] Ye D., Une remarque sur le comportement asymptotique des solutions de -Δu=λfu, C. R. Acad. Sci. Paris I 325 (1997) 1279-1282. | MR 1490413 | Zbl 0895.35014

[28] Ye D., Zhou F., A generalized two dimensional Emden-Fowler equation with exponential nonlinearity, Calc. Var. Partial Differential Equations 13 (2001) 141-158. | MR 1861095 | Zbl 1077.35048