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The work of Norman Dancer
On a degree associated with the Gross-Pitaevskii system with a large parameter
School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia |
In a number of cases we calculate the sum of the degrees of the small positive solutions of the Gross-Pitaevskii system when the interaction is strong.
References:
| [1] |
E. N. Dancer,
On the Dirichlet problem for weakly non-linear elliptic partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 76 (1976/77), 283-300.
doi: 10.1017/S0308210500019648. |
| [2] |
______, On the converse problem for the Gross-Pitaevskii equations with a large parameter,
Discrete Contin. Dyn. Syst., 34 (2014), 2481-2493.
doi: 10.3934/dcds.2014.34.2481. |
| [3] |
E. N. Dancer and Y. Du,
Competing species equations with diffusion, large interactions, and jumping nonlinearities, J. Differential Equations, 114 (1994), 434-475.
doi: 10.1006/jdeq.1994.1156. |
| [4] |
E. N. Dancer, K. Wang and Z. Zhang,
The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture, J. Funct. Anal., 262 (2012), 1087-1131.
doi: 10.1016/j.jfa.2011.10.013. |
| [5] |
S. Fučík, Boundary value problems with jumping nonlinearities, Časopis Pěst. Mat., 101 (1976), 69-87. |
| [6] |
B. Noris, H. Tavares, S. Terracini and G. Verzini,
Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302.
doi: 10.1002/cpa.20309. |
| [7] |
R. D. Nussbaum, Some generalizations of the Borsuk-Ulam theorem, Proc. London Math. Soc., (3), 35 (1977), 136-158.
doi: 10.1112/plms/s3-35.1.136. |
show all references
References:
| [1] |
E. N. Dancer,
On the Dirichlet problem for weakly non-linear elliptic partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 76 (1976/77), 283-300.
doi: 10.1017/S0308210500019648. |
| [2] |
______, On the converse problem for the Gross-Pitaevskii equations with a large parameter,
Discrete Contin. Dyn. Syst., 34 (2014), 2481-2493.
doi: 10.3934/dcds.2014.34.2481. |
| [3] |
E. N. Dancer and Y. Du,
Competing species equations with diffusion, large interactions, and jumping nonlinearities, J. Differential Equations, 114 (1994), 434-475.
doi: 10.1006/jdeq.1994.1156. |
| [4] |
E. N. Dancer, K. Wang and Z. Zhang,
The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture, J. Funct. Anal., 262 (2012), 1087-1131.
doi: 10.1016/j.jfa.2011.10.013. |
| [5] |
S. Fučík, Boundary value problems with jumping nonlinearities, Časopis Pěst. Mat., 101 (1976), 69-87. |
| [6] |
B. Noris, H. Tavares, S. Terracini and G. Verzini,
Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math., 63 (2010), 267-302.
doi: 10.1002/cpa.20309. |
| [7] |
R. D. Nussbaum, Some generalizations of the Borsuk-Ulam theorem, Proc. London Math. Soc., (3), 35 (1977), 136-158.
doi: 10.1112/plms/s3-35.1.136. |
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