On the mild solutions of higher-order differential equations in Banach spaces
Lan, Nguyen Thanh
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 865-880 / Harvested from Project Euclid
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For the higher-order abstract differential equation $u^{(n)}(t) = Au(t) +f(t)$ , $t\in \mathbb{R}$ , we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace $\mathcal{M}$ of $\mathrm{BUC}(\mathbb{R}, E)$ with respect to the above-mentioned equation in terms of solvability of the operator equation $AX-X\mathcal{D}^n = C$ . As applications, periodicity and almost periodicity of mild solutions are also proved.
Publié le : 2003-08-17
Classification:  34G10,  34K06,  47D06 
@article{1063629050,
     author = {Lan, Nguyen Thanh},
     title = {On the mild solutions of higher-order differential equations in Banach spaces},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 865-880},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1063629050}
}

Lan, Nguyen Thanh. On the mild solutions of higher-order differential equations in Banach spaces. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  865-880. http://gdmltest.u-ga.fr/item/1063629050/