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1

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

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

Difference equations with impulses

Danca Marius, Feckan Michal, Pospisil Michal

Opuscula Mathematica

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2019

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Vol. 39, no. 1

5--22

EN

Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.

5

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.

6

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.

7

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

Raja R., Sakthivel R., Anthoni S. M., Kim H.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 1

127-135

EN

The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as theMatlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

8

Oscillations of a higher order nonlinear differential equations with impulses

Wen -wen K., Wang G. Q., Cheng S. S.

Demonstratio Mathematica

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2010

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Vol. 43, nr 3

575-603

EN

Impulsive differential equations are important in simulation of processes with jump conditions. Although there are quite a few studies on the oscillation properties of low order equations, there are not too many studies of higher order equations. In this paper, we derive several oscillation criteria which are either new or improve several recent results in the literature. In addition, we provide several examples to illustrate the use of our results.