Abstract
We are interested in studying semilinear Cauchy problems in which the closed linear operator is not Hille-Yosida and its domain is not densely dened. Using integrated semigroup theory, we study the positivity of solutions to the semilinear problem, the Lipschitz perturba- tion of the problem, dierentiability of the solutions with respect to the state variable, time dierentiability of the solutions, and the stability of equilibria. The obtained results can be used to study several types of dif- ferential equations, including delay dierential equations, age-structure models in population dynamics, and evolution equations with nonlinear boundary conditions.
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