Periodic solutions of integro-differential equations in Banach space having Fourier type

The aim of this work is to study the existence of a periodic solutions of integro-differential equations d dt [x(t)-- L(x t)] = A[x(t)-- L(x t)]+ G(x t)+ t --$\infty$ a(t-- s)x(s)ds+ f (t), (0 $\le$ t $\le$ 2$\pi$) with the periodic condition x(0) = x(2$\pi$), where a $\in$ L 1 (R +). Our approach is based on the M-boundedness of linear operators, Fourier type, B s p,q-multipliers and Besov spaces.Comment: arXiv admin note: text overlap with arXiv:1707.0787

R-boundedness Approach to linear third differential equations in a UMD Space

The aim of this work is to study the existence of a periodic solutions of third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic condition $x(0) = x(2\pi), x'(0) = x'(2\pi)$ and $x''(0) = x''(2\pi)$. Our approach is based on the R-boundedness and $L^{p}$-multiplier of linear operators

Existence and uniqueness of functional differential equations with n delay

In this paper we give a necessary and suffcient conditions for the existence and uniqueness of periodic solutions of functional differential equations with n delay d dt x(t) = Ax(t) + n j=1 Bx(t -- r j) + f (t). The conditions are obtained in terms of R-boundedness of operator valued Fourier multipliers

Study of the microstructure of collapsible soil treated with the potassium chloride

The collapse of soils is a very complex phenomenon that involves a large number of intrinsic and environment parameters. This research aims to try to better understand the causes of collapse of soils and propose solutions to improve them and limit subsidence at least to an acceptable level. From a soil sample reconstituted in the laboratory, composed of a mixture (80% sand and 20% kaolin), we have shown the benefit of additions of salt solutions such as KCl. Analyses with scanning electron microscope and spectroscopy energy dispersive X-ray revealed microstructural changes and a significant interaction between clay particles and potassium chloride. The K+ cation is easily embedded in the pores and promotes the formation of a dense and compact material