Well‐posedness of degenerate differential equations with fractional derivative in vector‐valued functional spaces
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DOI: 10.1002/mana.201500481
Abstract: In this paper, we study the well-posedness of the degenerate differential equations with fractional derivative Dα(Mu)(t)=Au(t)+f(t),(0≤t≤2π) in Lebesgue–Bochner spaces Lp(T;X), periodic Besov spaces Bp,qs(T;X) and periodic Triebel–Lizorkin spaces Fp,qs(T;X), where A and M are closed… read more here.
Keywords: degenerate differential; well posedness; fractional derivative; posedness degenerate ... See more keywords
Hölder Continuous Solutions of Second Order Degenerate Differential Equations with Finite Delay
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DOI: 10.1007/s00025-019-0982-2
Abstract: In this paper, we characterize the $$C^\alpha $$Cα-well-posedness of the second order degenerate differential equation with finite delay $$(Mu)''(t) = Au(t) + Fu_t + f(t)$$(Mu)′′(t)=Au(t)+Fut+f(t), ($$t\in {\mathbb R}$$t∈R) by using known operator-valued Fourier multiplier results… read more here.
Keywords: order degenerate; finite delay; degenerate differential; second order ... See more keywords
Well-Posedness of Third Order Degenerate Differential Equations with Finite Delay in Banach Spaces
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DOI: 10.1007/s00025-021-01376-8
Abstract: In this paper, we give necessary and sufficient conditions for the $$L^p$$ -well-posedness (resp. $$B_{p,q}^s$$ -well-posedness) for the third order degenerate differential equation with finite delay: $$(Mu)'''(t) + (Nu)''(t)= Au(t) + Bu'(t) + Gu''_t +… read more here.
Keywords: order degenerate; degenerate differential; finite delay; well posedness ... See more keywords
Periodic solutions of fractional degenerate differential equations with delay in Banach spaces
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DOI: 10.1007/s11856-019-1884-4
Abstract: We characterize the Lp-well-posedness (resp. $$B_{p,q}^s$$ -well-posedness) for the fractional degenerate differential equations with finite delay: $$D^\alpha(Mu)(t)=Au(t)+Gu'_t+Fu_t+f(t),\;\;\;(t\in[0,2\pi]),$$ where α > 0 is fixed and A, M are closed linear operators in a Banach space X… read more here.
Keywords: degenerate differential; solutions fractional; differential equations; fractional degenerate ... See more keywords