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August  2009, 24(3): 731-761. doi: 10.3934/dcds.2009.24.731

Peak solutions for the Dirichlet problem of an elliptic system

E. N. Dancer 1, , Danielle Hilhorst 2, and  Shusen Yan 3,

1. 

School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
2. 

Laboratoire de Mathématiques, Université de Paris-Sud 11, Bat. 425, F-91405, Orsay-Cedex, France
3. 

School of Mathematics, Statistics and Computer Science, The University of New England, Armidale NSW 2351, Australia

Received  February 2008 Revised  June 2008 Published  April 2009

We study a system of elliptic equations arising from biology with a chemotaxis term. This system is non-variational. Using a reduction argument, we show that the system has solutions with peaks near the boundary and inside the domain.
Keywords: Peak solution, Elliptic system, Non-variational..
Mathematics Subject Classification: Primary: 35J50; Secondary: 93C1.
Citation: E. N. Dancer, Danielle Hilhorst, Shusen Yan. Peak solutions for the Dirichlet problem of an elliptic system. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 731-761. doi: 10.3934/dcds.2009.24.731
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