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

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.

Show me the PDF file (212K), TEX file, and other files for this article.

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

Return to the EJDE web page