Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation

Juncheng Wei; Dong Ye; Feng Zhou

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 3, page 425-447
  • ISSN: 0294-1449

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Wei, Juncheng, Ye, Dong, and Zhou, Feng. "Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation." Annales de l'I.H.P. Analyse non linéaire 25.3 (2008): 425-447. <http://eudml.org/doc/78796>.

@article{Wei2008,
author = {Wei, Juncheng, Ye, Dong, Zhou, Feng},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {boundary bubble; blow-up analysis; localized energy method; Emden-Fowler equation},
language = {eng},
number = {3},
pages = {425-447},
publisher = {Elsevier},
title = {Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation},
url = {http://eudml.org/doc/78796},
volume = {25},
year = {2008},
}

TY - JOUR
AU - Wei, Juncheng
AU - Ye, Dong
AU - Zhou, Feng
TI - Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 3
SP - 425
EP - 447
LA - eng
KW - boundary bubble; blow-up analysis; localized energy method; Emden-Fowler equation
UR - http://eudml.org/doc/78796
ER -

References

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  1. [1] Bandle C., Flucher M., Harmonic radius and concentration of energy hyperbolic radius and Liouville’s equations Δ U = e U and Δ U = U ( n + 2 ) / ( n - 2 ) , SIAM Rev.38 (2) (1996) 191-238. Zbl0857.35034MR1391227
  2. [2] Baraket S., Pacard F., Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations6 (1) (1998) 1-38. Zbl0890.35047MR1488492
  3. [3] Brezis H., Merle F., Uniform estimates and blow-up behavior for solutions of - Δ u = V x e u in two dimensions, Comm. Partial Differential Equations16 (8–9) (1991) 1223-1253. Zbl0746.35006MR1132783
  4. [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. Zbl0745.76001MR1145596
  5. [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. Zbl0840.76002MR1362165
  6. [6] Chandrasekhar S., An Introduction to the Study of Stellar Structure, Dover, New York, 1957. Zbl0079.23901MR92663
  7. [7] Chanillo S., Kiessling M., Surfaces with prescribed Gauss curvature, Duke Math. J.105 (2) (2000) 309-353. Zbl1023.53005MR1793614
  8. [8] Chen W., Li C., Classification of solutions of some nonlinear elliptic equations, Duke Math. J.63 (1991) 615-623. Zbl0768.35025MR1121147
  9. [9] Del Pino M., Kowalczyk M., Musso M., Singular limits in Liouville-type equations, Calc. Var. Partial Differential Equations24 (2005) 47-81. Zbl1088.35067MR2157850
  10. [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 Linéaire22 (2005) 227-257. Zbl1129.35376MR2124164
  11. [11] Gelfand I.M., Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl.29 (1963) 295-381. Zbl0127.04901MR153960
  12. [12] Gidas B., Ni W.M., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979) 209-243. Zbl0425.35020MR544879
  13. [13] Joseph D.D., Lundgren T.S., Quasilinear problems driven by positive sources, Arch. Rat. Mech. Anal.49 (1973) 241-269. Zbl0266.34021MR340701
  14. [14] Li Y.Y., Harnack type inequality: the method of moving planes, Comm. Math. Phys.200 (1999) 421-444. Zbl0928.35057MR1673972
  15. [15] Li Y.Y., Shafrir I., Blow-up analysis for solutions of - Δ u = V e u in dimension two, Indiana Univ. Math. J.43 (4) (1994) 1255-1270. Zbl0842.35011MR1322618
  16. [16] Lin S.S., Positive radial solutions and non-radial bifurcation for semilinear elliptic equations in annular domains, J. Differential Eqnuations86 (1990) 367-391. Zbl0734.35073MR1064016
  17. [17] Lin C.S., Topological degree for mean field equations on S 2 , Duke Math. J.104 (3) (2000) 501-536. Zbl0964.35038MR1781481
  18. [18] Ma L., Wei J., Convergence for a Liouville equation, Comm. Math. Helv.76 (2001) 506-514. Zbl0987.35056MR1854696
  19. [19] Mignot F., Murat F., Puel J.P., Variation d'un point retournement par rapport au domaine, Comm. Partial Differential Equations4 (1979) 1263-1297. Zbl0422.35039MR546644
  20. [20] Mizoguchi N., Suzuki T., Equations of gas combustion: S-shaped bifurcation and mushrooms, J. Differential Equations134 (1997) 183-215. Zbl0876.35037MR1432094
  21. [21] Nagasaki K., Suzuki T., Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearities, Asymptotic Anal.3 (1990) 173-188. Zbl0726.35011MR1061665
  22. [22] Nagasaki K., Suzuki T., Radial solutions for Δ u + λ e u = 0 on annuli in higher dimensions, J. Differential Equations100 (1992) 137-161. Zbl0776.35047MR1187866
  23. [23] Pacard F., Radial and non-radial solutions of - Δ u = λ f u on an annulus of R n , n 3 , J. Differential Equations101 (1993) 103-138. Zbl0799.35089MR1199485
  24. [24] Pohozaev S.I., Eigenfunctions of the equation Δ u + λ f u = 0 , Soviet Math. Dokl.6 (1965) 1408-1411. Zbl0141.30202MR192184
  25. [25] Senba T., Suzuki T., Some structures of the solution set from stationary system of chemotaxis, Adv. Math. Sci. Appl.10 (2000) 191-224. Zbl0999.35031MR1769174
  26. [26] Wei J., Ye D., Zhou F., Bubbling solutions for an anisotropic Emden–Fowler equation, Calc. Var. Partial Differential Equations28 (2007) 217-247. Zbl1159.35402MR2284567
  27. [27] Ye D., Une remarque sur le comportement asymptotique des solutions de - Δ u = λ f u , C. R. Acad. Sci. Paris I325 (1997) 1279-1282. Zbl0895.35014MR1490413
  28. [28] Ye D., Zhou F., A generalized two dimensional Emden–Fowler equation with exponential nonlinearity, Calc. Var. Partial Differential Equations13 (2001) 141-158. Zbl1077.35048MR1861095

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