On the boundary spike layer solutions to a singularly perturbed neumann problem

Journal of Differential Equations

Volumn 134, Issue 1, 1997, Pages 104-133

  Juncheng, Wei ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031562011     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.3218     Document Type: Article

References (23)

1. 1. S. Agmon, "Lectures on Elliptic Boundary Value Problems," Von Nostrand, Princeton, 1965.
2. 2. Adimurthi, G. Mancinni, and S. L. Yadava, The role of mean curvature in a semilinear Neumann problem involving the critical Sobolev exponent, Comm. Partial Differential Equations 20 (1995), 591-631.
3. 3. 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.
4. ∞-estimates for solutions involving the critical Sobolev exponent, Differential Integral Equation 8, No. 1 (1995), 41-68.
5. 5. A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetik 12 (1972), 30-39.
6. n, in "Mathematical Analysis and Applications," Part. A, Adv. Math. Suppl. Studies, Vol. 7A, pp. 369-402, Academic Press, New York, 1981.
7. n, Arch. Rational Mech. Anal. 105 (1989), 243-266.
8. 8. C.-S. Lin, W.-M. Ni, and I. Takagi, Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations 72 (1988), 1-27.
9. 9. 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.
10. 10. W.-M. Ni and I. Takagi, On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math. 41 (1991), 819-851.
11. 11. W.-M. Ni and I. Takagi, Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993), 247-281.
12. 12. W.-M. Ni and I. Takagi, Point-condensation generated be a reaction-diffusion system in axially symmetric domains, Japan J. Indust. Appl. Math. 12 (1995), 327-365.
13. 13. W.-M. Ni and J. Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995), 731-768.
14. 14. X. B. Pan, Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations 8 (1995), 1-36.
15. 15. X. B. Pan, Condensation of least-energy solutions: The effect of boundary conditions, Nonlinear Anal. TMA 24 (1995), 195-222.
16. 16. X. B. Pan, Further study on the effect of boundary conditions, J. Differential Equations 117 (1995), 446-468.
17. 17. X. B. Pan and X. F. Wang, Semilinear Neumann problem in an exterior domain, preprint.
18. 18. X. B. Pan and Xing-Wang Xu, Least energy solutions of semilinear Neumann problems and asymptotics, J. Math. Anal. Appl., to appear.
19. 19. I. Takagi, Point-condensation for a reaction-diffusion system, J. Differential Equations 61 (1986), 208-249.
20. 20. I. Takagi and J. Wei, in preparation.
21. 21. Z.-Q. Wang, On the existence of multiple single-peaked solutions for a semilinear Neumann problem, Arch. Rational Mech. Anal. 120 (1992), 375-399.
22. 22. J. Wei, On the construction of single-peaked solutions of a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996), 315-333.
23. 23. J. Wei, On the effect of the domain geometry in a singularly perturbed Dirichlet problem, preprint.