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1
Content available Karakostas fixed point theorem and semilinear neutral differential equations with impulses and nonlocal conditions
Leiva Hugo, Riera Lenin, Lalvay Sebastián
Journal of Mathematics and Applications
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2022
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Vol. 45
107--128
EN
This paper is concerned with the existence and uniqueness of solutions for a semilinear neutral differential equation with impulses and nonlocal conditions. First, we assume that the nonlinear terms are locally Lipschitz, and to achieve the existence of solutions, Karakostas Fixed Point Theorem is applied. After that, under some additional conditions, the uniqueness is proved as well. Next, assuming some bound on the non-linear terms the global existence is proved by applying a generalization of Gronwall inequality for impulsive differential equations. Then, we suppose stronger hypotheses on the nonlinear functions, such as globally Lipschitz conditions, that allow us to appy Banach Fixed Point Theorem to prove the existence and uniqueness of solutions. Finally, we present an example as an application of our method.
2
Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
Hellal Meryem, Merzagui N.
Journal of Applied Analysis
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2020
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Vol. 26, nr 2
193--207
EN
In this work, we use the fixed-point theorem in double cones to study the existence of multiple positive solutions for an impulsive first-order differential system with integral boundary conditions, when the nonlinearities change sign.
3
Content available remote Scalar linear impulsive Riemann-Liouville fractional differential equations with constant delay-explicit solutions and finite time stability
Hristova Snezhana G., Tersian Stepan A.
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
121--130
EN
Riemann-Liouville fractional differential equations with a constant delay and impulses are studied in this article. The following two cases are considered: the case when the lower limit of the fractional derivative is fixed on the whole interval of consideration and the case when the lower limit of the fractional derivative is changed at any point of impulse. The initial conditions as well as impulsive conditions are defined in an appropriate way for both cases. The explicit solutions are obtained and applied to the study of finite time stability.
4
Content available Nonlinear fractional differential equations with non-instantaneous impulses in Banach spaces
Benchohra M., Slimane M.
Journal of Mathematics and Applications
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2018
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Vol. 41
39--51
EN
This paper is devoted to study the existence of solutions for a class of initial value problems for non-instantaneous impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Monch's fixed point theorem and the technique of measures of noncompactness.
5
Content available remote Rozkłady: prąd aktywny, prąd rozrzutu, prąd bierny w dziedzinie czasu - podstawy matematyczne, metoda operatorowa
Siwczyński M.
Przegląd Elektrotechniczny
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2011
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R. 87, nr 4
134-141
PL
W artykule podano podstawy matematyczne rachunku operatorowego L-impulsów i sygnałów okresowych. Takie podejście umożliwia identyfikację zjawisk energetycznych w obwodach elektrycznych bezpośrednio w dziedzinie czasu. W szczególności dotyczy to kwestii rozkładu prądu odbiornika na składowe fizyczne.
EN
In the article the mathematical theory of the operational calculus of the L- impulses and periodical signals are presented. Was shown that this approach makes identification of power phenomena in electrical circuit in the time domain: the distribution of current to physical components in special case.
6
Content available Kształtowanie elektrochemiczne łopatki sekwencją procesów ECM-PECM
Kozak J.
Inżynieria Maszyn
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2011
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R. 16, z. 4
68-74
PL
W pracy przedstawiono kształtowanie elektrochemiczne pióra łopatki lotniczych silników turbinowych w dwu kolejnych zabiegach, a mianowicie obróbki prądem ciągłym ECM i prądem impulsowym PECM. Omówiono zadania cząstkowe niezbędne w projektowaniu i optymalizacji technologii elektrochemicznej Wykazano, że dokładność wymiarową ECM/PECM można poprawić utrzymując małą szczelinę pomiędzy elektrodami.
EN
Electrochemical machining using continuous and pulse current (ECM, PECM) provides an economical and effective method for machining high strength, heat-resistant materials into complex shapes such as airfoils of titanium alloys. The dimensional accuracy of ECM/PECM can be improved if a small interelectrode gap is maintained. This paper presents the manufacturing of airfoils by sequences both treatments ECM and PECM.
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