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

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 18, Issue 2, 2001, Pages 157-178

  Catrina, Florin ^a   Wang, Zhi Qiang ^a  

^a UTAH STATE UNIVERSITY   (United States)

Author keywords

Degenerate elliptic equations; Local minimizations; Positive solutions; Prescribed symmetry

Indexed keywords

EID: 0347872973     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(00)00061-5     Document Type: Article

References (30)

1. Aubin T., Problèmes isopérimétriques de Sobolev, J. Differential Geom. 11 (1976) 573-598.
2. Berestycki H., Esteban M., Existence and bifurcation of solutions for an elliptic degenerate problem, J. Differential Equations 134 (1997) 1-25.
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.
4. Byeon J., Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli, J. Differential Equations 136 (1997) 136-165.
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.
6. Caffarelli L.A., Kohn R., Nirenberg L., First order interpolation inequalities with weights, Compositio Mathematica 53 (1984) 259-275.
7. Caldiroli P., Musina R., On the existence of extremal functions for a weighted Sobolev embedding with critical exponent, Cal. Var. and PDEs 8 (1999) 365-387.
8. Catrina F., Wang Z.-Q., Nonlinear elliptic equations on expanding symmetric domains, J. Differential Equations 156 (1999) 153-181.
9. Catrina F., Wang Z.-Q., On the Caffarelli-Kohn-Nirenberg inequalities, C. R. Acad. Sci. Paris Sér. I Math. 300 (2000) 437-442.
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.
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.
12. Coffman C.V., A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984) 429-437.
13. Dautray R., Lions J.-L., Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Springer-Verlag, Berlin, 1985.
14. n, Adv. Math., Suppl. Studies 7A (1981) 369-402.
15. Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998.
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.
17. Kawohl B., Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., Vol. 1150, Springer, 1985.
18. n, Arch. Rat. Mech. Anal. 105 (1989) 243-266.
19. Li Y.Y., Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equations 83 (1990) 348-367.
20. Lieb E.H., Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. Math. 118 (1983) 349-374.
21. Lions P.-L., Concentration compactness principle in the calculus of variations. The locally compact case. Part 1, Ann. Inst. H. Poincaré Anal. Nonlinéaire 1 (1984) 109-145.
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.
23. Mizoguchi N., Suzuki T., Semilinear elliptic equations on annuli in three and higher dimensions, Houston J. Math. 1 (1996) 199-215.
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.
25. Palais R., The principle of symmetric criticality, Comm. Math. Phys. 69 (1979) 19-30.
26. Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pure Appl. 110 (1976) 353-372.
27. Wang Z.-Q., Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations 159 (1999) 102-137.
28. Wang Z.-Q., Willem M., Singular minimization problems, J. Differential Equations 161 (2000) 307-320.
29. Willem M., Minimax Theorems, Birkhäuser, Boston, 1996.
30. Willem M., A decomposition lemma and critical minimization problems, preprint.