Convergent solutions of certain nonlinear differential equations with maxima

González, Patricio Aroca; Pinto, Manuel

doi:10.1016/j.mcm.2005.03.008

Cited by 6 publications

(3 citation statements)

References 7 publications

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“…Differential equations with maximum have proved to be strong tools in the modelling of many physical problems: systems with automatic regulation, problems in control theory that correspond to the maximal deviation of the regulated quantity etc.. As a consequence there was an intensive development of the theory of differential equations with "maxima" [2,5,6,[8][9][10][11][12][13][14] etc..…”

Section: Indroductionmentioning

confidence: 99%

A relaxation theorem for a differential inclusion with “maxima”

Cernea

2017

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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We consider a Cauchy problem associated to a nonconvex differential inclusion with "maxima" and we prove a Filippov type existence result. This result allows to obtain a relaxation theorem for the problem considered. IndroductionDifferential equations with maximum have proved to be strong tools in the modelling of many physical problems: systems with automatic regulation, problems in control theory that correspond to the maximal deviation of the regulated quantity etc.. As a consequence there was an intensive development of the theory of differential equations with "maxima" [2,5,6,[8][9][10][11][12][13][14] etc..A classical example is the one of an electric generator ([2]). In this case the mechanism becomes active when the maximum voltage variation is reached in an interval of time. The equation describing the action of the regulator has the form x (t) = ax(t) + b maxwhere a, b are constants given by the system, x(.) is the voltage and f (.) is a perturbation given by the change of voltage. In this paper we study the following problem x (t) ∈ F (t, x(t), max

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Section: Indroductionmentioning

confidence: 99%

A relaxation theorem for a differential inclusion with “maxima”

Cernea

2017

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…For example, many problems in the control theory correspond to the maximal deviation of the regulated quantity. Some qualitative properties of the solutions of ordinary differential equations with "maxima" can be found in [1][2][3][4] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Integral Stability in Terms of Two Measures for Nonlinear Differential Systems with “Maxima”

Wang

Liu

2014

Abstract and Applied Analysis

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“…One special class of functional differential equations that has many applications in the mathematical simulation of some systems with automatic regulation [16] are differential equations with maximum. Recently, Bainov and Vulov [3,22] have formulated some mathematical models of differential equations with maximum and interesting results about the stability using a modification of Lyapunov's first method were obtained; theorems for existence, uniqueness and continuability are proved in [2,3,7,11,14]; some oscillation results are obtained in [4]; the averaging method is justified in [15]. However, so far the problem for the stability of the solutions of such equations by means of Lyapunov-Razumikhin method have not been considered.…”

Section: Introductionmentioning

confidence: 99%