| Contents |
| We consider the existence of positive steady states of nonlinear
evolution equations arising in structured population dynamics. Often
these problems can be reduced to an eigenvector problem for a
parameterized family of unbounded linear operators plus a finite
dimensional fixed point problem for a (in general) set-valued map.
When the vital rates are monotonous functions of the interaction
variables this map is single-valued and the existence of equilibria
can be established by standard procedures. In the general case, some
results can be obtained in the case of two dimensional
nonlinearities [1]. As an example, we will consider the case of a
selection mutation equation for the density of individuals with
respect to an evolutionary trait, namely the age at maturity, and
with respect to physiological age ([2]).
[1] A. Calsina, J. Farkas, Positive steady states of structured population models with finite dimensional nonlinearities. Submitted
[2] A. Calsina and J. M. Palmada, Steady states of a selection-mutation model for an age
structured population, J. Math. Anal. Appl., 400 (2013), 386-395. |
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