Stability Properties of Positive Solutions to Partial Differential Equations with Delay
Simon, Peter L
Southwest Texas State University, Department of Mathematics
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.
Semilinear equations with delay, Stability of stationary solutions, Convex nonlinearity, concave nonlinearity
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.