Multipeak solutions for a singularly perturbed Neumann problem

Pacific Journal of Mathematics

Volumn 189, Issue 2, 1999, Pages 241-262

  Dancer, E N ^a   Yan, Shusen ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000650326     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.1999.189.241     Document Type: Article

References (21)

1. Adimurthi, G. Mancini and S.L. Yadava, The role of mean curvature in a semilinear Neumann problem involving the critical Sobolev exponent, Comm. P.D.E., 20 (1995), 591-631.
2. Adimurthi, F. Pacella and S.L. Yadava, Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Funct. Anal., 113 (1993), 318-350.
3. A. Bahri, Critical points at infinity in some variational problems, Research Notes in Mathematics, 182, Longman-Pitman, 1989.
4. A. Bahri and J.M. Coron, On a nonlinear elliptic equation involving the Sobolev exponent: The effect of the topology of the domain, Comm. Pure Appl. Math., 41 (1988), 253-294.
5. P. Bates, E.N. Dancer and J. Shi, Multi-spike stationary solutions on the Cahn-Hilliard equation in higher demension and instability, preprint.
6. D. Cao, E.N. Dancer, E. Noussair and S. Yan, On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems, Discrete and Continuous Dynamical Systems, 2 (1996), 221-236.
7. n, Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Studies, 7A, Academic Prees, New York.
8. C. Gui, Multipeak solutions for a semilinear Neumann problem, Duke Math. J., 84 (1996), 739-769.
9. n, Arch. Rat. Mech. Anal., 105 (1989), 243-266.
10. Y.Y. Li, On a singularly perturbed equation with Neumann boundary condition, preprint.
11. H. Meinhardt, Models of biological pattern formation, Academic Press, 1982.
12. W.M. Ni, X. Pan and I. Takagi, Singular behavior of least-energy solutions of a semilinear Neumann Problem involving critical Sobolev exponents, Duke Math. J., 67 (1992), 1-20.
13. W.M. Ni and I. Takagi, On the shape of the least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 41 (1991), 819-851.
14. _, Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J., 70 (1993), 247-281.
15. O. Rey, The role of the Green's function in a non-linear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal., 89 (1990), 1-52.
16. _, Boundary effect for an elliptic Neumann problem with critical nonlinearity, Comm. P.D.E., 22 (1997), 1055-1139.
17. Z.Q. Wang, On the existence of multiple single-peaked solution for a semilinear Neumann problem, Arch. Rat. Mech. Anal., 120 (1992), 375-399.
18. _, The effect of the domain geometry on the number of positive solutions of Neumann problems with critical exponents, Diff. Int. Equations, 8 (1995), 1533-1554.
19. _, High energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponent, Proc. Royal Soc. Edinburgh, 125A (1995), 1003-1029.
20. _, Construction of multi-peaked solution for a nonlinear Neumann problem with critical exponent, Nonlinear Anal. T.M.A., 27 (1996), 1281-1306.
21. J.Wei, On the boundary spike layer solutions to a singularly perturbed Neumann problem, J. Diff. Equation, 134 (1997), 104-133.