Electron. J. Diff. Eqns., Vol. 2001(2001), No. 64, pp. 1-8.

Stability properties of positive solutions to partial differential equations with delay

Gyula Farkas & Peter L. Simon

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.

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Gyula Farkas
Department of Mathematics
Istvan Szechenyi College
H-9026 Gyor, Hedervariu. 3., Hungary
P{rof. Gyula Farkas died in a traffic accident in Lisbon
on February 27, 2002.
Peter L. Simon
School of Chemistry
University of Leeds
Leeds LS2 9JT, UK
e-mail: peters@chem.leeds.ac.uk

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