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__a230,
     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__a230/}
}
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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__a230/