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
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On semilinear Cauchy problems with non-dense domain. / Magal, Pierre; Ruan, Shigui.
In: Advances in Differential Equations, Vol. 14, No. 11-12, 2009, p. 1041-1084.Research output: Contribution to journal › Article
}
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 -