Abstract
We are basically concerned with existence of standing pulse solutions for an elliptic equation with a nonlocal term. The problem comes from an activator-inhibitor system such as the FitzHugh-Nagumo equations with inhibitor’s diffusion or arises in the Allen-Cahn equation with the nonlocal term. We prove it mathematically rigorously in a bounded domainΩ ⊂R n (n ≥ 2) with smooth boundary, by employing the Lyapunov-Schmidt reduction method, which is the same kind of way as used typically in [2], [9], [10], [13], for instance.
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Oshita, Y., Ohnishi, I. Standing pulse solutions for the FitzHugh-Nagumo equations. Japan J. Indust. Appl. Math. 20, 101 (2003). https://doi.org/10.1007/BF03167465
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DOI: https://doi.org/10.1007/BF03167465