Geodesic
Linear Functional-Differential Equations in a Banach Algebra*
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 435-439

Voir la notice de l'article provenant de la source Cambridge University Press

The theory of analytic differential systems in Banach algebras has been investigated by E. Hille and others, see for instance Chapter 6 in [4].In this paper we show how a projection method used by W. A. Harris, Jr., Y. Sibuya, and L. Weinberg [3] can be applied to study a class of functional differential equations in this setting. The method, based on functional analysis, had been used extensively by L. Cesari [1] in similar forms for boundary value problems, and by J. K. Hale, S. Bancroft, and D. Sweet [2]. We also obtain as corollaries several results for ordinary differential equations in Banach algebras which were proved in a different way by Hille. 
Fitzpatrick, W. J.; Grimm, L. J. Linear Functional-Differential Equations in a Banach Algebra*. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 435-439. doi: 10.4153/CMB-1978-076-3
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[1] 1. Cesari, L., Functional analysis and an alternative method. Michigan Math. J. 11, (1964), 385-414. Google Scholar

[2] 2. Hale, J. K., Bancroft, S., and Sweet, D., Alternative problems for nonlinear functional equations. J. Differential Equations 4, (1968), 40-56. Google Scholar

[3] 3. Harris, W. A. Jr., Sibuya, Y., and Weinberg, L., Holomorphic solutions of linear differential systems at singular points, Arch. Rat. Mech. Anal. 35, (1969), 245-248. Google Scholar

[4] 4. Hille, E., Lectures on Ordinary Differential Equations, Addison-Wesley, Reading, Mass., 1969. Google Scholar

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