Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in RN

Florin Catrina; Zhi-Qiang Wang

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 2, page 157-178
  • ISSN: 0294-1449

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Catrina, Florin, and Wang, Zhi-Qiang. "Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in RN." Annales de l'I.H.P. Analyse non linéaire 18.2 (2001): 157-178. <http://eudml.org/doc/78516>.

@article{Catrina2001,
author = {Catrina, Florin, Wang, Zhi-Qiang},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {positive solutions; degenerate elliptic equations; local minimization},
language = {eng},
number = {2},
pages = {157-178},
publisher = {Elsevier},
title = {Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in RN},
url = {http://eudml.org/doc/78516},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Catrina, Florin
AU - Wang, Zhi-Qiang
TI - Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in RN
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 2
SP - 157
EP - 178
LA - eng
KW - positive solutions; degenerate elliptic equations; local minimization
UR - http://eudml.org/doc/78516
ER -

References

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  1. [1] Aubin T, Problèmes isopérimétriques de Sobolev, J. Differential Geom.11 (1976) 573-598. Zbl0371.46011MR448404
  2. [2] Berestycki H, Esteban M, Existence and bifurcation of solutions for an elliptic degenerate problem, J. Differential Equations134 (1997) 1-25. Zbl0870.34032MR1429089
  3. [3] Brezis H, Lieb E.H, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc.88 (1983) 486-490. Zbl0526.46037MR699419
  4. [4] Byeon J, Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli, J. Differential Equations136 (1997) 136-165. Zbl0878.35043MR1443327
  5. [5] Caffarelli L.A, Gidas B, Spruck J, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math.42 (1989) 271-297. Zbl0702.35085MR982351
  6. [6] Caffarelli L.A, Kohn R, Nirenberg L, First order interpolation inequalities with weights, Compositio Mathematica53 (1984) 259-275. Zbl0563.46024MR768824
  7. [7] Caldiroli P, Musina R, On the existence of extremal functions for a weighted Sobolev embedding with critical exponent, Cal. Var. and PDEs8 (1999) 365-387. Zbl0929.35045MR1700269
  8. [8] Catrina F, Wang Z.-Q, Nonlinear elliptic equations on expanding symmetric domains, J. Differential Equations156 (1999) 153-181. Zbl0944.35026MR1701798
  9. [9] Catrina F, Wang Z.-Q, On the Caffarelli–Kohn–Nirenberg inequalities, C. R. Acad. Sci. Paris Sér. I Math.300 (2000) 437-442. Zbl0954.35050
  10. [10] Catrina F., Wang Z.-Q., On the Caffarelli–Kohn–Nirenberg inequalities: sharp constants, existence (and nonexistence) and symmetry of extremal functions, Comm. Pure Appl. Math., in press. Zbl1072.35506
  11. [11] Chou K.S, Chu C.W, On the best constant for a weighted Sobolev–Hardy inequality, J. London Math. Soc.2 (1993) 137-151. Zbl0739.26013
  12. [12] Coffman C.V, A nonlinear boundary value problem with many positive solutions, J. Differential Equations54 (1984) 429-437. Zbl0569.35033MR760381
  13. [13] Dautray R, Lions J.-L, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Springer-Verlag, Berlin, 1985. Zbl0683.35001MR1036731
  14. [14] Gidas B, Ni W.-M, Nirenberg L, Symmetry of positive solutions of nonlinear elliptic equations in Rn, Adv. Math., Suppl. Studies7A (1981) 369-402. Zbl0469.35052MR634248
  15. [15] Gilbarg D, Trudinger N.S, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998. Zbl0361.35003
  16. [16] Horiuchi T, Best constant in weighted Sobolev inequality with weights being powers of distance from the origin, J. Inequal. Appl.1 (1997) 275-292. Zbl0899.35034MR1731336
  17. [17] Kawohl B, Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., 1150, Springer, 1985. Zbl0593.35002MR810619
  18. [18] Kwong M.K, Uniqueness of positive solutions of Δu−u+up=0 in Rn, Arch. Rat. Mech. Anal.105 (1989) 243-266. Zbl0676.35032
  19. [19] Li Y.Y, Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equations83 (1990) 348-367. Zbl0748.35013MR1033192
  20. [20] Lieb E.H, Sharp constants in the Hardy–Littlewood–Sobolev and related inequalities, Ann. Math.118 (1983) 349-374. Zbl0527.42011
  21. [21] Lions P.-L, Concentration compactness principle in the calculus of variations. The locally compact case. Part 1, Ann. Inst. H. Poincaré Anal. Nonlinéaire1 (1984) 109-145. Zbl0541.49009MR778970
  22. [22] Lions P.-L, Concentration compactness principle in the calculus of variations. The limit case. Part 1, Rev. Mat. Ibero.1.1 (1985) 145-201. Zbl0704.49005MR834360
  23. [23] Mizoguchi N, Suzuki T, Semilinear elliptic equations on annuli in three and higher dimensions, Houston J. Math.1 (1996) 199-215. Zbl0862.35036MR1434392
  24. [24] Ni W.-M, Takagi I, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math.45 (1991) 819-851. Zbl0754.35042MR1115095
  25. [25] Palais R, The principle of symmetric criticality, Comm. Math. Phys.69 (1979) 19-30. Zbl0417.58007MR547524
  26. [26] Talenti G, Best constant in Sobolev inequality, Ann. Mat. Pure Appl.110 (1976) 353-372. Zbl0353.46018MR463908
  27. [27] Wang Z.-Q, Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations159 (1999) 102-137. Zbl1005.35083MR1726920
  28. [28] Wang Z.-Q, Willem M, Singular minimization problems, J. Differential Equations161 (2000) 307-320. Zbl0954.35074MR1744147
  29. [29] Willem M, Minimax Theorems, Birkhäuser, Boston, 1996. Zbl0856.49001MR1400007
  30. [30] Willem M., A decomposition lemma and critical minimization problems, preprint. Zbl1194.35122MR2056515

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