Stationary solutions of reaction‐diffusion equations

摘要

AbstractGiven a semilinear reaction‐diffusion equation. If the corresponding ordinary differential equation admits a convex compact positively invariant set and the boundary data assume their values in this set then the first and third boundary value problem have stationary solutions. The proofs are based on Weinberger's strong invariance principle, some related tools and the Leray‐Schauder degree. The theorem is applied to several equations from theoretical biology, also in the case of distinct diffusion ra