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Integrated Semigroups and Delay Differential Equations

open access: yesJournal of Mathematical Analysis and Applications, 1993
The idea of integrated semigroup is associated with the study of the evolution equation (1) \(du/dt=Au\), where \(A\) does not satisfy all of the assumptions of the famous Hille-Yosida theorem. In such a setting integrating both sides of (1) from 0 to \(t\) we obtain a strongly continuous family of operators (not a semigroup) which is the integral of ...
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The nonnegativity of solutions of delay differential equations

open access: yesApplied Mathematics Letters, 2000
In this paper, the author proves the nonnegativity of solutions to delay equations of the type \[ x'(t)=F(x(t))+G(x(t-\tau)) \] under certain conditions. A few examples are discussed.
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