297 research outputs found
Boundedness and Stability of Impulsively Perturbed Systems in a Banach Space
Consider a linear impulsive equation in a Banach space
with . Suppose each solution of
the corresponding semi-homogeneous equation
(2) is bounded for any bounded sequence .
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
and bounded sequence ;
(c) for any tending to
zero;
(d) exponential estimate of implies a similar estimate for .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
Global stability of sets for impulsive differential-difference equations by Lyapunov's direct method
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
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