### 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 defined. Using integrated semigroup theory, we study the positivity of solutions to the semilinear problem, the Lipschitz perturbation of the problem, diffierentiability of the solutions with respect to the state variable, time diffierentiability of the solutions, and the stability of equilibria. The obtained results can be used to study several types of differential equations, including delay diffierential equations, age-structure models in population dynamics, and evolution equations with nonlinear boundary conditions.

Original language | English (US) |
---|---|

Pages (from-to) | 1041-1084 |

Number of pages | 44 |

Journal | Advances in Differential Equations |

Volume | 14 |

Issue number | 11-12 |

State | Published - 2009 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Advances in Differential Equations*,

*14*(11-12), 1041-1084.

**On semilinear Cauchy problems with non-dense domain.** / Magal, Pierre; Ruan, Shigui.

Research output: Contribution to journal › Article

*Advances in Differential Equations*, vol. 14, no. 11-12, pp. 1041-1084.

}

TY - JOUR

T1 - On semilinear Cauchy problems with non-dense domain

AU - Magal, Pierre

AU - Ruan, Shigui

PY - 2009

Y1 - 2009

N2 - 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, diffierentiability of the solutions with respect to the state variable, time diffierentiability of the solutions, and the stability of equilibria. The obtained results can be used to study several types of differential equations, including delay diffierential equations, age-structure models in population dynamics, and evolution equations with nonlinear boundary conditions.

AB - 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, diffierentiability of the solutions with respect to the state variable, time diffierentiability of the solutions, and the stability of equilibria. The obtained results can be used to study several types of differential equations, including delay diffierential equations, age-structure models in population dynamics, and evolution equations with nonlinear boundary conditions.

UR - http://www.scopus.com/inward/record.url?scp=77950636584&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950636584&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77950636584

VL - 14

SP - 1041

EP - 1084

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 11-12

ER -