WELL-POSEDNESS OF DEGENERATE DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN HÖLDER CONTINUOUS FUNCTION SPACES

2019 ◽  
Vol 9 (1) ◽  
pp. 187-199
Author(s):  
Shangquan Bu ◽  
◽  
Gang Cai ◽  
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Infinite Delay ◽  
Function Spaces ◽  
Well Posedness ◽  
Hölder Continuous ◽  
Degenerate Differential Equations

Well-posedness of Third Order Differential Equations in Hölder Continuous Function Spaces

2018 ◽  
Vol 62 (4) ◽  
pp. 715-726
Author(s):  
Shangquan Bu ◽  
Gang Cai
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Function Spaces ◽  
Linear Operators ◽  
Well Posedness ◽  
Third Order ◽  
Hölder Continuous ◽  
Vector Valued ◽  
Closed Linear Operators

AbstractIn this paper, by using operator-valued ${\dot{C}}^{\unicode[STIX]{x1D6FC}}$-Fourier multiplier results on vector-valued Hölder continuous function spaces, we give a characterization of the $C^{\unicode[STIX]{x1D6FC}}$-well-posedness for the third order differential equations $au^{\prime \prime \prime }(t)+u^{\prime \prime }(t)=Au(t)+Bu^{\prime }(t)+f(t)$, ($t\in \mathbb{R}$), where $A,B$ are closed linear operators on a Banach space $X$ such that $D(A)\subset D(B)$, $a\in \mathbb{C}$ and $0<\unicode[STIX]{x1D6FC}<1$.

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