A FUNCTIONAL ANALYTIC PERSPECTIVE TO DELAY DIFFERENTIAL EQUATIONS

作者：Picard Rainer^*; Trostorff Sascha; Waurick Marcus

来源：Operators and Matrices, 2014, 8(1): 217-236.

DOI：10.7153/oam-08-12

• Ordinary differential equations
• causality
• memory
• delay.

We generalize the solution theory for a class of delay type differential equations developed in a previous paper, dealing with the Hilbert space case, to a Banach space setting. The key idea is to consider differentiation as an operator with the whole real line as the underlying domain as a means to incorporate pre-history data. We focus our attention on the issue of causality of the differential equations as a characterizing feature of evolutionary problems and discuss various examples. The arguments mainly rely on a variant of the contraction mapping theorem and a few well-known facts from functional analysis.

• 出版日期2014-3