Existence and uniqueness of solutions on bounded domains to a FitzHugh–Nagumo type elliptic system

Carolus Reinecke and Guido Sweers

Vol. 197 (2001), No. 1, 183–211

DOI: 10.2140/pjm.2001.197.183

Abstract

In this paper we prove the existence and uniqueness of the boundary layer solution to a semilinear eigenvalue problem consisting of a coupled system of two elliptic partial differential equations. Although the system is not quasimonotone, there exists a transformation to a quasimonotone system. For the transformed system we may and will use maximum (sweeping) principle arguments to derive pointwise estimates. A degree argument completes the uniqueness proof.

Milestones

Received: 15 February 1999

Revised: 3 August 1999

Published: 1 January 2001