Stability Properties of Positive Solutions to Partial Differential Equations with Delay
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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.
CitationFarkas, G., & Simon, P. L. (2001). Stability properties of positive solutions to partial differential equations with delay. Electronic Journal of Differential Equations, 2001(64), pp. 1-8.
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