Geodesic
Stability properties of positive solutions to partial differential equations with delay
Electronic journal of differential equations, Tome 2001 (2001)
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.
Classification : 35R10, 35B99
Keywords: semilinear equations with delay, stability of stationary solutions, convex nonlinearity, concave nonlineariry 
@article{EJDE_2001__2001__a74,
     author = {Farkas,  Gyula and Simon,  Peter L.},
     title = {Stability properties of positive solutions to partial differential equations with delay},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0993.35086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a74/}
}
TY  - JOUR
AU  - Farkas,  Gyula
AU  - Simon,  Peter L.
TI  - Stability properties of positive solutions to partial differential equations with delay
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a74/
LA  - en
ID  - EJDE_2001__2001__a74
ER  - 
%0 Journal Article
%A Farkas,  Gyula
%A Simon,  Peter L.
%T Stability properties of positive solutions to partial differential equations with delay
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a74/
%G en
%F EJDE_2001__2001__a74
Farkas,  Gyula; Simon,  Peter L. Stability properties of positive solutions to partial differential equations with delay. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a74/