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

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  • 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.
    Mathematics Subject Classification: Primary: 34B18; Secondary: 34C23, 34E20, 37G10.


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