Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.3, pp.19--22

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 3, pp.19--22

Ladder Theorems and Positivity of Solutions for Dissipative Partial Differential Equations.
M. V. Bartuccelli

We obtain ladder estimates for semilinear dissipative differential equations. Then we use these estimates to find conditions which assure that solutions with positive initial data are (at least) eventually (i.e. asymptotically) positive. These results are of fundamental importance in many fields of applied mathematics as, for example, biological dynamics, where the solutions of the equations modelling the systems under investigation must often be positive functions.

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