On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem

Royal Society of Edinburgh - Proceedings A

Volumn 127, Issue 4, 1997, Pages 691-701

  Dancer, E N ^a   Wei, Juncheng ^b  

^a UNIVERSITY OF SYDNEY   (Australia)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744457514     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500023775     Document Type: Article

References (16)

1. D. G. Aronson and H. F. Weinberger. Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 30 (1978), 33-76.
2. P. Clement and G. Sweers. Existence and multiplicity results for semilinear elliptic eigenvalue problem. Ann. Scuola Norm. Sup. Pisa 14 (1987), 97-121.
3. E. N. Dancer. On the number of positive solutions of weakly elliptic problems when a parameter is large. Proc. London Math. Soc. 53 (1986), 429-52.
4. E. N. Dancer. On positive solutions of some singularly perturbed problems when the nonlinearity changes sign. Topol. Methods Nonlinear Anal. 5 (1995), 141-75.
5. E. N. Dancer. A note on asymptotic uniqueness for some nonlinearities which change sign (Preprint, University of Sydney, 1995).
6. E. N. Dancer. Some singularly perturbed problems on annulus and a counterexample to a problem of Gidas, Ni and Nirenberg (to appear in Bull. London Math. Soc.).
7. B. Gidas, W.-M. Ni and L. Nirenberg. Symmetry and related properties via the Maxiumum Principle. Comm. Math. Phys. 68(3) (1979), 209-43.
8. n. Mathematical Analysis and Applications, Part A. Adv. Math. Suppl. Studies 7A (1981), 369-402.
9. D. Gilbarg and N. S. Trudinger. Elliptic partial differential equations of second order, 2nd edn (Berlin: Springer, 1983).
10. H. Hofer. Variational and topological methods in partially ordered Hilbert space. Math. Ann. 261 (1982), 493-514.
11. J. Jang. On spike solutions of singularly perturbed Dirichlet problems. J. Differential Equations 114 (1994), 370-95.
12. P. Korman, Y. Li and T. Ouyang. Exact multiplicity results for boundary value problems with nonlinearities generalizing cubic. SIAM J. Math. Anal. (to appear).
13. W.-M. Ni and I. Takagi. Locating the peaks of least-energy solutions to a semilinear Neumann problem. Duke Math. J. 70 (1993), 247-81.
14. W.-M. Ni and J. Wei. On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem. Comm. Pure Appl. Math. 48 (1995), 731-68.
15. W.-M. Ni, I. Takagi and J. Wei. On the location and profile of intermediate solutions to a singularly perturbed semilinear Dirichlet problem (Preprint).
16. N. Arch. Rational Mech. Anal. 81 (1993), 247-81.