| Volume 9, Number 1, 2019, Pages 187-199 DOI：10.11948/2019.187 |
| {Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces |
| Shangquan Bu,Gang Cai |
| Keywords:${C}^\alpha$-well-posedness, degenerate differential equations, infinite delay, $\dot{C}^\alpha$-Fourier multiplier, Holder continuous function spaces. |
| Abstract: |
| Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)""(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), 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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