Volume 9, Number 1, 2019, Pages 187199 DOI：10.11948/2019.187 
{Wellposedness of degenerate differential equations with infinite delay in Holder continuous function spaces 
Shangquan Bu,Gang Cai 
Keywords:${C}^\alpha$wellposedness, degenerate differential equations, infinite delay, $\dot{C}^\alpha$Fourier multiplier, Holder continuous function spaces. 
Abstract: 
Using operatorvalued $\dot{C}^\alpha$Fourier multiplier results on vector valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$wellposedness of the first order degenerate differential equations with infinite delay $(Mu)""(t) = Au(t) + \int_{\infty}^t a(ts)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$. 
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