Stability Properties of Positive Solutions to Partial Differential Equations with Delay
Date
2001-10-08
Authors
Farkas, Gyula
Simon, Peter L
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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 ƒ(0) ≤ 0 implies instability and in the concave case ƒ(0) ≥ 0 implies stability. Special cases are shown where the monotonicity assumption can be weakened or omitted.
Description
Keywords
Semilinear equations with delay, Stability of stationary solutions, Convex nonlinearity, concave nonlinearity
Citation
Farkas, G., & Simon, P. L. (2001). Stability properties of positive solutions to partial differential equations with delay. <i>Electronic Journal of Differential Equations, 2001</i>(64), pp. 1-8.
Rights
Attribution 4.0 International