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 domain Ω ⊂ Rn (n ≥ 2) with smooth boundary, by employing the Lyapunov-Schmidt reduction method, which is the same kind of way as used typically in , , , , for instance.
|Number of pages||15|
|Journal||Japan Journal of Industrial and Applied Mathematics|
|Publication status||Published - Feb 2003|
- Standing pulse solutions
- The FitzHugh-Nagumo equations
ASJC Scopus subject areas
- Applied Mathematics