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Proceedings of the London Mathematical Society 2005 90(1):209-244; doi:10.1112/S0024611504014947
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© London Mathematical Society

Multipeak Solutions for the Neumann Problem of an Elliptic System of Fitzhugh–Nagumo Type

E. N. Dancer and Shusen Yan

School of Mathematics and Statistics, University of Sydney NSW 2006, Australia. E-mail: normd{at}maths.usyd.edu.au
School of Mathematics and Statistics, University of Sydney NSW 2006, Australia. E-mail: shusen{at}maths.usyd.edu.au

Received 5 September 2003. Revision received 10 March 2004.

For systems of elliptic equations of Fitzhugh–Nagumo type on bounded domains and with small diffusion in one equation, we construct solutions with multiple sharp peaks close to each other and close to, but not on, the boundary. This is a striking contrast to results for scalar equations.

For some symmetric domains, we also construct similar multipeak solutions except that here the peaks are not close to each other. 2000 Mathematics Subject Classification 35J50 (primary), 93C15 (secondary).

This work was supported by the ARC.


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