Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 64, pp. 1-8.

Title:  Stability properties of positive solutions to partial
        differential equations with delay
   
Authors: Gyula Farkas (Istvan Szechenyi College, Hungary)
         Peter L. Simon (Univ. of Leeds, Leeds, UK)
         
Abstract:  
  We  investigate the stability of positive stationary solutions of
 semilinear initial-boundary value problems with delay and convex 
 or concave nonlinearity. If the nonlinearity is monotone, 
 then in the convex case $f(0)\le 0$ implies instability and  
 in the concave case $f(0)\ge 0$ implies stability. 
 Special cases are shown where the monotonicity assumption can 
 be weakened or omitted. 

Submitted June 21, 2001. Published October 8, 2001.
Math Subject Classifications: 35R10, 35B99.
Key Words: 
semilinear  equations with delay; stability of stationary 
            solutions; convex nonlinearity; concave nonlineariry.