Existence and uniqueness of solutions on bounded domains to a FitzHugh–Nagumo type elliptic system
Carolus J. Reinecke, Guido H. Sweers · Pacific Journal of Mathematics · 2001
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.