Solutions of Second-Order Integro-Differential Equations on Periodic Besov Spaces

Abstract

Maximal regularity for an integro-differential equation with infinite delay on periodic vectorvalued Besov spaces is studied. We use Fourier multipliers techniques to characterize periodic solutions solely in terms of spectral properties on the data. We study a resonance case obtaining a compatibility condition which is necessary and sufficient for the existence of periodic solutions.

Periodic solutions of degenerate differential equations in vector-valued function spaces

“…See e.g. [8], [9], [10], [23], [24], [28] and references therein. For one side, the main novelty in this paper relies in the presence of two non-commuting operators A and M , that are only related by the domain.…”

B-separable anisotropic convolution operators and applications

“…The maximal regularity of this problem in mixed B s p;q norm is obtained. In this direction we can mention, e.g., [3,7,12]. Let Q D R n , where R is an open connected set with compact C 2m -boundary @ .…”

“…Moreover, convolutiondifferential equations (CDEs) have been investigated, e.g., in [7,12,13,15,17] and the references therein. However, convolution differential-operator equations (CDOEs) are relatively a less studied subject.…”

Maximal regularity for perturbed integral equations on periodic Lebesgue spaces

“…Maximal regularity on periodic Lebesgue, Besov and Triebel spaces for the subject of integrodifferential equations, and by use of operator-valued Fourier multiplier theorems, have been studied recently in [11,[21][22][23][24]29]. Our case is more difficult to handle because of the presence of the perturbing operator B.…”