Structural properties of functional differential equations in Banach spaces. (English) Zbl 0713.34069

Nakagiri, Shin-ichi

Osaka J. Math. 25, No. 2, 353-398 (1988).

The treatment of functional differential equations in the state space \({\mathbb{R}}^ n\times L^ p([-n,0],{\mathbb{R}}^ n)\) initiated by C. Bernier and A. Manitius [Can. J. Math. 30, 897-914 (1978; Zbl 0368.47026)] is extended to Banach space valued equations. The associated semigroups and the structural operators are investigated and a spectral theory including the completeness of generalized eigenfunctions is developped. Applications to partial differential equations with delay conclude the paper.

Reviewer: R.Nagel

MSC:

34K99	Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34G10	Linear differential equations in abstract spaces
47D06	One-parameter semigroups and linear evolution equations

Keywords:

functional differential equations; Applications; partial differential equations with delay