# American Institute of Mathematical Sciences

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2013, 2013(special): 467-476. doi: 10.3934/proc.2013.2013.467

## Bifurcation structure of steady-states for bistable equations with nonlocal constraint

 1 Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585 2 Department of Applied Physics, University of Miyazaki, Miyazaki, 889-2192

Received  September 2012 Revised  April 2013 Published  November 2013

This paper studies the 1D Neumann problem of bistable equations with nonlocal constraint. We obtain the global bifurcation structure of solutions by a level set analysis for the associate integral mapping. This structure implies that solutions can form a saddle-node bifurcation curve connecting boundary-layer states with internal-layer states. Furthermore, we exhibit the applications of our result to a couple of shadow systems arising in surface chemistry and physiology.
Citation: Kousuke Kuto, Tohru Tsujikawa. Bifurcation structure of steady-states for bistable equations with nonlocal constraint. Conference Publications, 2013, 2013 (special) : 467-476. doi: 10.3934/proc.2013.2013.467
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