Boundedness and Stability of Impulsively Perturbed Systems in a Banach Space

Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty$. Suppose each solution of the corresponding semi-homogeneous equation $$\dot{x}(t)+A(t)x(t) = 0,$$ (2) is bounded for any bounded sequence $\{ \alpha_i \}$. The conditions are determined ensuring (a) the solution of the corresponding homogeneous equation has an exponential estimate; (b) each solution of (1),(2) is bounded on the half-line for any bounded $f$ and bounded sequence $\{ \alpha_i \}$ ; (c) $\lim_{t \rightarrow \infty}x(t)=0$ for any $f, \alpha_i$ tending to zero; (d) exponential estimate of $f$ implies a similar estimate for $x$.Comment: 19 pages, LaTex-fil

Estimates of solutions of impulsive parabolic equations and applications to the population dynamics

A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given

Asymptotic equivalence of impulsive differential equations in a Banach space

By means of Schauder's fixed point theorem sufficient conditions for asymptotic equivalence of impulsive equations in a Banach space are found

Estimates for the Cauchy matrix of perturbed linear impulsive equation

Estimates for the Cauchy matrix of a perturbed linear impulsive equation are obtained for given estimates for the Cauchy matrix of the corresponding unperturbed linear impulsive equation

On the oscillatory properties of the solutions of a class of integro-differential equations of neutral type

In the present paper the oscillatory properties of the solutions of the equation[(Lx)(t)](n)+∫ItK(t,s,x(s))ds=0are investigated where n≥1, L is an operator of the difference type, It⊂ℝ, K:DK→ℝ, DK⫅ℝ3, x:[αx,∞]→ℝ. Under natural conditions imposed on L, It and K it is proved that for n even all ultimately nonzero solutions oscillate and for n odd they either oscillate or tend to zero as t→∞

Magnetron sputtering in rigid optical solar reflectors production

Magnetron sputtering was applied to meet the growing need for glass optical solar reflectors. This plasma method provided more uniform deposition of the silver based coating on glass substrates resulted in decrease of defective reflectors fraction down to 5%. For instance, such parameter of resistive evaporation was of 30%. Silver film adhesion to glass substrate was enhanced with indium tin oxide sublayer. Sunlight absorption coefficient of these rigid reflectors was 0.081-0.083

Solution and Asymptotic Behavior for a Nonlocal Coupled System of Reaction-Diffusion

This paper concerns with existence, uniqueness and asymptotic behavior of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is presented