1 results
Hölder Continuous Solutions of Degenerate Differential Equations with Finite Delay
-
- Journal:
- Canadian Mathematical Bulletin / Volume 61 / Issue 2 / 01 June 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 240-251
- Print publication:
- 01 June 2018
-
- Article
-
- You have access
- Export citation
-
Using known operator-valued Fourier multiplier results on vector-valued Hölder continuous function spaces
${{C}^{\alpha }}(\mathbb{R};\,X)$, we completely characterize the 
${{C}^{\alpha }}$-well-posedness of the first order degenerate differential equations with finite delay 
$(Mu{)}'(t)\,=\,Au(t)\,+\,F{{u}_{t}}\,+\,f(t)$ for 
$t\,\in \,\mathbb{R}$ by the boundedness of the 
$(M,\,F)$-resolvent of A under suitable assumption on the delay operator 
$F$, where 
$A,M$ are closed linear operators on a Banach space 
$X$ satisfying 
$D(A)\,\cap \,D(M)\,\ne \,\{0\}$, the delay operator $F$ is a bounded linear operator from 
$C([-r,0];X)$ to $X$, and 
$r\,>\,0$ is fixed.
