Results 21 to 30 of about 39,621 (275)
Stratified discontinuous differential equations and sufficient conditions for robustness [PDF]
, 2015 International audienceThis paper is concerned with state-constrained discontinuous ordinary differential equations for which the corresponding vector field has a set of singularities that forms a stratification of the state domain. Existence of solutions
Hermosilla, Cristopher
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A Survey of Recent Results for the Generalizations of Ordinary Differential Equations
Abstract and Applied Analysis, 2014 This is a review paper on recent results for different types of generalized ordinary differential equations. Its scope ranges from discontinuous equations to equations on time scales. We also discuss their relation with inclusion and highlight the use of
Daniel C. Biles +2 more
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Non-autonomous scalar discontinuous ordinary differential equation
Journal of Mathematical Analysis and Applications, 2005 A scalar differential equation is considered. The right-hand side of the equation represents a sum of a discontinuous function \(f(x)\) and a function \(h(t)\). The functions \(f\) and \(h\) are nonnegative, \(f\) is finite a.e. and \(1/f\) and \(h\) are Lebesgue integrable. The existence of a local absolutely continuous solution is proved. The authors
Pikuta, Piotr, Rzymowski, Witold
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Electronic Journal of Qualitative Theory of Differential Equations, 2017 We use upper and lower absolutely continuous functions as subsolutions and supersolutions to discontinuous ordinary differential equations. We present sufficient conditions for the existence of extremal solutions to initial value problems. Due to a new
Krzysztof Topolski
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Dynamics at a switching intersection:hierarchy, isonomy, and multiple-sliding [PDF]
, 2014 If a set of ordinary differential equations is discontinuous along some thresh- old, solutions can be found that are continuous, if sometimes multi-valued.
Jeffrey, Mike R
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The stability of Cohen–Grossberg neural networks with time dependent delays
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023 Background. The study is devoted to the analysis of stability in the sense Lyapunov Cohen-Grossberg neural networks with time-dependent delays. To do this, we study the stability of the steady-state solutions of systems of linear differential equations ...
Il'ya V. Boykov +2 more
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Some applications of Laplace transforms in models with impulses or discontinuous forcing functions [PDF]
Revista Brasileira de Ensino de FísicaCommonly, in Ordinary Differential Equations courses, equations with impulses or discontinuous forcing functions are studied. In this context, the Laplace Transform of the Dirac delta function and unit step function is taught, which are used as forcing ...
Diego Miranda Gonçalves +1 more
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Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation. [PDF]
PLoS ONE, 2012 In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential ...
Kun Wei +3 more
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APPROXIMATION OF POSITIONAL IMPULSE CONTROLS FOR DIFFERENTIAL INCLUSIONS
Ural Mathematical Journal, 2022 Nonlinear control systems presented as differential inclusions with positional impulse controls are investigated. By such a control we mean some abstract operator with the Dirac function concentrated at each time. Such a control ("running impulse"), as a
Ivan A. Finogenko, Alexander N. Sesekin
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On numerical solution of ordinary differential equations with discontinuities [PDF]
Applications of Mathematics, 1988 The author considers the initial value problem for the system of ordinary differential equations (1) \(y'=f(t,y)\), \(y(a)=y_ 0\) on \(I=\) where the function f is of Caratheodory's type and satisfies the Perron condition. A bounded function x is a solution of (1) if it is absolutely continuous on I, satisfies the initial condition and the equation ...
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