# American Institute of Mathematical Sciences

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

## Peak solutions for the Dirichlet problem of an elliptic system

 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.
Citation: E. N. Dancer, Danielle Hilhorst, Shusen Yan. Peak solutions for the Dirichlet problem of an elliptic system. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 731-761. doi: 10.3934/dcds.2009.24.731
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