Conditional Lipschitz Shadowing for Ordinary Differential Equations
Journal of Dynamics and Differential Equations, 2023 AbstractWe introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain nonautonomous ordinary differential equations have such a property.
Lucas Backes +3 more
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On compactness and connectedness of the paratingent
, 2016 In this note we shall prove that for a continuous function \(\varphi : \Delta\to\mathbb{R}^n\), where \(\Delta\subset\mathbb{R}\), the paratingent of \(\varphi\) at \(a\in\Delta\) is a non-empty and compact set in \(\mathbb{R}^n\) if and only if ...
Zygmunt, Wojciech
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Approximate solutions of hybrid stochastic pantograph equations with Levy jumps [PDF]
, 2013 We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. We prove that the approximate solutions converge to the true solutions in 퐿 2 sense as well as in probability under local Lipschitz condition ...
Mao, Wei +3 more
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Estimates for iterated commutators of multilinear square fucntions with Dini-type kernels
Journal of Inequalities and Applications, 2018 Let TΠb→ $T_{\Pi\vec {b}}$ be the commutator generated by a multilinear square function and Lipschitz functions with kernel satisfying Dini-type condition.
Zengyan Si, Qingying Xue
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A lower lipschitz condition for the stable subordinator [PDF]
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1971 lim sup _ 1 ~ o oz ...
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On Lipschitz ball noncollapsing functions and uniform co-Lipschitz mappings of the plane
Abstract and Applied Analysis, 2005 We give a sharp estimate on the cardinality of point preimages of a uniform co-Lipschitz mapping on the plane. We also give a necessary and sufficient condition for a ball noncollapsing Lipschitz function to have a point with infinite preimage.
Olga Maleva
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Numerical solutions of neutral stochastic functional differential equations
, 2008 This paper examines the numerical solutions of neutral stochastic functional differential equations (NSFDEs) $d[x(t)-u(x_t)]=f(x_t)dt+g(x_t)dw(t)$, $t\geq 0$.
Wu, Fuke +5 more
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Existence and Continuous Dependence for Fractional Partial Hyperbolic Differential Equations
Journal of Function Spaces, 2015 This paper is concerned with a class of fractional hyperbolic partial differential equations with the Caputo derivative. Existence and continuous dependence results of solutions are obtained under the hypothesis of the Lipschitz condition without any ...
Qixiang Dong, Guangxian Wu, Lanping Zhu
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Uniqueness theorem of differential system with coupled integral boundary conditions
Electronic Journal of Qualitative Theory of Differential Equations, 2018 The paper is devoted to study the uniqueness of solutions for a differential system with coupled integral boundary conditions under a Lipschitz condition. Our approach is based on the Banach's contraction principle.
Yujun Cui +3 more
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Causal‐Guided Ultra‐Long‐Term Time Series Forecasting Via Anticipated Covariates
Advanced Science, EarlyView.Often treated as unknown, information from the future remains underutilized.We demonstrate that in a coupled dynamical system, providing the future state of the effect enables accurate forecasting of the cause for a long timesteps. A time series forecasting paradigm that introduces anticipated covariates to represent such known future states is ...
Jintong Zhao +4 more
wiley +1 more source