Advances in Differential Equations

On semilinear Cauchy problems with non-dense domain

Pierre Magal and Shigui Ruan

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

Article information

Adv. Differential Equations Volume 14, Number 11/12 (2009), 1041-1084.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations 45D05: Volterra integral equations [See also 34A12] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Magal, Pierre; Ruan, Shigui. On semilinear Cauchy problems with non-dense domain. Adv. Differential Equations 14 (2009), no. 11/12, 1041--1084.

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