Existence and nonexistence of G - Least energy solutions for a nonlinear Neumann problem with critical exponent in symmetric domains

Calculus of Variations and Partial Differential Equations

Volumn 8, Issue 2, 1999, Pages 109-122

  Wang, Zhi Qiang ^a  

^a UTAH STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000610793     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050119     Document Type: Article

References (21)

1. [AM] Adimurthi, Mancini G., The Neumann problem for elliptic equations with critical non-linearity, A tribute in honor of G.Prodi, Scuola Norm. Sup. Pisa (1991), 9-25.
2. [APY] Adimurthi, Pacella F., Yadava S.L., Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Func. Anal. 113 (1993), 318-350.
3. [Au] Aubin T., Nonlinear Analysis on Manifold: Monge-Ampere Equations, New York, Springer-Verlag (1982).
4. [BN] Brezis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math. 36 (1983), 437-477.
5. [GT] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Second Edition, Springer-Verlag, 1983.
6. [GP] Grossi M., Pacella F., Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions, Proc. Roy. Soc. Edinburgh 116A (1990), 23-43.
7. [L1] Lions P.L., The concentration-compactness principle in the calculus of variations, The locally compact case, Part 1 and Part 2, Ann. Inst. H. Poincaré Anal. Nonlinéaire 1 (1984), 109-145, 223-283.
8. [L2] Lions P.L., The concentration-compactness principle in the calculus of variations, The limit case, Rev. Mat. Ibero americana, 1 (1985), 145-201 and 2 (1985), 45-121.
9. [L2] Lions P.L., The concentration-compactness principle in the calculus of variations, The limit case, Rev. Mat. Ibero americana, 1 (1985), 145-201 and 2 (1985), 45-121.
10. [MSW] Maier S., Schmitt K., Wang Z.-Q., On Neumann problems for semilinear elliptic equations with critical nonlinearity: existence and symmetry of multi-peaked solutions, Comm. in PDEs, 22 (1997), 1493-1527.
11. [NPT] Ni W.-M., Pan X.-B., Takagi I., Singular behavior of least energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J. 67 (1992), 1-20.
12. [NT1] 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.
13. [NT2] Ni W.-M., Takagi I., Locating the peaks of least-energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993), 247-281.
14. [P] Palais R., The principle of symmetric criticality. Comm. Math. Phys. 69 (1979), 19-30.
15. [S] Struwe M., Variational Methods, Springer-Verlag, New York, 1990.
16. [T] Talenti G., Best constants in Sobolev inequality, Annali di Mat. 110 (1976), 353-372.
17. [Wx] Wang X.-J., Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Diff. Equ. 93 (1991), 283-310.
18. [Wz1] Wang Z.-Q., On the shape of solutions for a nonlinear Neumann problem in symmetric domains, Lectures in Applied Math. 29 (1993), 433-442.
19. [Wz2] Wang Z.-Q., High energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponent, Proc. Roy. Soc. Edinburgh 125A (1995), 1003-1029.
20. [Wz3] Wang Z.-Q., The effect of the domain geometry on the number of positive solutions of Neumann problems with critical exponents, Diff. and Integ. Equa. 8 (1995), 1533-1554.
21. [Wz4] Wang Z.-Q., Construction of multi-peaked solutions for a nonlinear Neumann problem with critical exponent in symmetric domains, Nonlinear Anal. TMA 27 (1996), 1281-1306.