Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces

• Autorzy: Shangquan Bu , Yi Fang
• Języki publikacji: EN

Abstrakty

EN

We study the maximal regularity on different function spaces of the second order integro-differential equations with infinite delay
$(P) u''(t) + αu'(t) + d/dt (∫^{t}_{-∞} b(t-s)u(s)ds) = Au(t) - ∫^{t}_{-∞} a(t-s)Au(s)ds + f(t)$
(0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), u'(0) = u'(2π), where A is a closed operator in a Banach space X, α ∈ ℂ, and a,b ∈ L¹(ℝ₊). We use Fourier multipliers to characterize maximal regularity for (P). Using known results on Fourier multipliers, we find suitable conditions on the kernels a and b under which necessary and sufficient conditions are given for the problem (P) to have maximal regularity on $L^{p}(𝕋,X)$, periodic Besov spaces $B_{p,q}^{s}(𝕋,X)$ and periodic Triebel-Lizorkin spaces $F_{p,q}^{s}(𝕋,X)$

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 47D99: None of the above, but in this section
• 45N05: Abstract integral equations, integral equations in abstract spaces
• 45D05: Volterra integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 184
• Numer: 2
• Strony: 103-119

Daty

wydano

2008

Twórcy

autor

Shangquan Bu

• Department of Mathematical Science, University of Tsinghua, Beijing 100084, China

autor

Yi Fang

• Department of Mathematical Science, University of Tsinghua, Beijing 100084, China

Identyfikatory

DOI

10.4064/sm184-2-1