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Journal articles on the topic 'Stabilité Lipschitz'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Grunert, Katrin, and Matthew Tandy. "Lipschitz stability for the Hunter–Saxton equation." Journal of Hyperbolic Differential Equations 19, no. 02 (2022): 275–310. http://dx.doi.org/10.1142/s0219891622500072.

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We study Lipschitz stability in time for [Formula: see text]-dissipative solutions to the Hunter–Saxton equation, where [Formula: see text] is a constant. We define metrics in both Lagrangian and Eulerian coordinates, and establish Lipschitz stability for those metrics.

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2

Soliman, A. A. "On eventual stability of impulsive systems of differential equations." International Journal of Mathematics and Mathematical Sciences 27, no. 8 (2001): 485–94. http://dx.doi.org/10.1155/s0161171201005622.

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The notions of Lipschitz stability of impulsive systems of differential equations are extended and the notions of eventual stability are introduced. New notions called eventual and eventual Lipschitz stability. We give some criteria and results.

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3

Fu, Yu Li. "On Lipschitz stability for F.D.E." Pacific Journal of Mathematics 151, no. 2 (1991): 229–35. http://dx.doi.org/10.2140/pjm.1991.151.229.

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4

Pilyugin, Sergei Yu, and Sergey Tikhomirov. "Lipschitz shadowing implies structural stability." Nonlinearity 23, no. 10 (2010): 2509–15. http://dx.doi.org/10.1088/0951-7715/23/10/009.

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5

Jiang, Zuohai, and Shicheng Xu. "Stability of Pure Nilpotent Structures on Collapsed Manifolds." International Mathematics Research Notices 2020, no. 24 (2019): 10317–45. http://dx.doi.org/10.1093/imrn/rnz023.

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Abstract The goal of this paper is to study the stability of pure nilpotent structures on an $n$-manifold for different collapsed metrics. We prove that if two metrics with bounded sectional curvature are $L_0$-bi-Lipschitz equivalent and sufficient collapsed (depending on $L_0$ and $n$), then up to a diffeomorphism, the underlying nilpotent Killing structures coincide with each other, or one is embedded into another as a subsheaf. It improves Cheeger–Fukaya–Gromov’s local compatibility of pure nilpotent Killing structures for one collapsed metric to two Lipschitz equivalent metrics. As an app

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6

Chu, Chin-Ku, Myung-Sun Kim, and Keon-Hee Lee. "Lipschitz stability and Lyapunov stability in dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 19, no. 10 (1992): 901–9. http://dx.doi.org/10.1016/0362-546x(92)90102-k.

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7

Martynyuk, A. A. "On integral stability and Lipschitz stability of motion." Ukrainian Mathematical Journal 49, no. 1 (1997): 84–92. http://dx.doi.org/10.1007/bf02486618.

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8

Gracia, Juan-Miguel, and Francisco E. Velasco. "Lipschitz stability of controlled invariant subspaces." Linear Algebra and its Applications 434, no. 4 (2011): 1137–62. http://dx.doi.org/10.1016/j.laa.2010.10.024.

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9

Chu, Chin-Ku, and Keon-Hee Lee. "Embedding of Lipschitz stability in flows." Nonlinear Analysis: Theory, Methods & Applications 26, no. 11 (1996): 1749–52. http://dx.doi.org/10.1016/0362-546x(95)00014-m.

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10

Soliman, A. A. "Lipschitz stability with perturbing liapunov functionals." Applied Mathematics Letters 17, no. 8 (2004): 939–44. http://dx.doi.org/10.1016/j.aml.2003.10.008.

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11

KLEMENT, ERICH PETER, ANNA KOLESÁROVÁ, RADKO MESIAR, and ANDREA STUPŇANOVÁ. "LIPSCHITZ CONTINUITY OF DISCRETE UNIVERSAL INTEGRALS BASED ON COPULAS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18, no. 01 (2010): 39–52. http://dx.doi.org/10.1142/s0218488510006374.

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The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization of stochastically increasing Archimedean copulas is also given.

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12

Murty, K. N., and Michael D. Shaw. "Stability analysis of nonlinear Lyapunov systems associated with an nth order system of matrix differential equations." Journal of Applied Mathematics and Stochastic Analysis 15, no. 2 (2002): 141–50. http://dx.doi.org/10.1155/s104895330200014x.

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This paper introduces the notion of Lipschitz stability for nonlinear nth order matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear nth order matrix Lyapunov differential system. We study observability and controllability of a special system of nth order nonlinear Lyapunov systems.

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13

Wang, Yingying, and Zhinan Xia. "Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications." Mathematics 11, no. 9 (2023): 2006. http://dx.doi.org/10.3390/math11092006.

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For generalized ordinary differential equations, sufficient criteria are given for the Lipschitz stability in terms of two measures of the trivial solutions. As an application, we apply our main results by studying the Lipschitz stability for measure differential equations and impulsive differential equations. Compared to the classical ones, the conditions here regarding the functions are more general.

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14

Rong, Xiaochun, та Shicheng Xu. "Stability of eϵ-Lipschitz and co-Lipschitz maps in Gromov–Hausdorff topology". Advances in Mathematics 231, № 2 (2012): 774–97. http://dx.doi.org/10.1016/j.aim.2012.05.018.

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15

Dragičević, Davor. "Weighted Hyers-Ulam Stability for Nonlinear Nonautonomous Difference Equations." Sarajevo Journal of Mathematics 18, no. 1 (2024): 97–106. http://dx.doi.org/10.5644/sjm.18.01.07.

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Let $(A_m)_{m\in \mathbb{Z}}$ be a sequence of bounded linear operators acting on an arbitrary Banach space $X$ and admitting an exponential dichotomy. Furthermore, let $f_m \colon X\to X$, $m\in \mathbb{Z}$ be a sequence of Lipschitz maps. Provided that the Lipschitz constants of $f_m$ are uniformly small, we show that a nonlinear difference equation $x_{m+1} = A_mx_m +f_m(x_m), m\in \mathbb{Z}$ exhibits various types of the Hyers-Ulam stability property.

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16

Montoya, Cristhian. "Inverse source problems for the Korteweg–de Vries–Burgers equation with mixed boundary conditions." Journal of Inverse and Ill-posed Problems 27, no. 6 (2019): 777–94. http://dx.doi.org/10.1515/jiip-2018-0108.

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Abstract In this paper, we prove Lipschitz stability results for the inverse source problem of determining the spatially varying factor in a source term in the Korteweg–de Vries–Burgers (KdVB) equation with mixed boundary conditions. More precisely, the Lipschitz stability property is obtained using observation data on an arbitrary fixed sub-domain over a time interval. Secondly, we show that stability property can also be achieved from boundary measurements. Our proofs relies on Carleman inequalities and the Bukhgeim–Klibanov method.

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17

Ledrappier, F., and L. S. Young. "Stability of Lyapunov exponents." Ergodic Theory and Dynamical Systems 11, no. 3 (1991): 469–84. http://dx.doi.org/10.1017/s0143385700006283.

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AbstractWe consider small random perturbations of matrix cocycles over Lipschitz homeomorphisms of compact metric spaces. Lyapunov exponents are shown to be stable provided that our perturbations satisfy certain regularity conditions. These results are applicable to dynamical systems, particularly to volume-preserving diffeomorphisms.

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18

Higham, Desmond J., Xuerong Mao, and Andrew M. Stuart. "Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations." LMS Journal of Computation and Mathematics 6 (2003): 297–313. http://dx.doi.org/10.1112/s1461157000000462.

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AbstractPositive results are proved here about the ability of numerical simulations to reproduce the exponential mean-square stability of stochastic differential equations (SDEs). The first set of results applies under finite-time convergence conditions on the numerical method. Under these conditions, the exponential mean-square stability of the SDE and that of the method (for sufficiently small step sizes) are shown to be equivalent, and the corresponding second-moment Lyapunov exponent bounds can be taken to be arbitrarily close. The required finite-time convergence conditions hold for the c

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19

Protasov, V. Yu. "Lipschitz stability of operators in Banach spaces." Proceedings of the Steklov Institute of Mathematics 280, no. 1 (2013): 268–79. http://dx.doi.org/10.1134/s0081543813010203.

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20

Bainov, D. d., and I. m. Stamova. "Lipschitz stability of impulsive functional-differential equations." Applicable Analysis 73, no. 3-4 (1999): 393–405. http://dx.doi.org/10.1080/00036819908840787.

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21

Sincich, E. "Lipschitz stability for the inverse Robin problem." Inverse Problems 23, no. 3 (2007): 1311–26. http://dx.doi.org/10.1088/0266-5611/23/3/027.

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22

Janin, Robert, and Jacques Gauvin. "Lipschitz-Type Stability in Nonsmooth Convex Programs." SIAM Journal on Control and Optimization 38, no. 1 (1999): 124–37. http://dx.doi.org/10.1137/s0363012996298990.

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23

Przesławski, Krzysztof. "Lipschitz selections and stability for quasiconvex programs." Journal of Mathematical Analysis and Applications 274, no. 2 (2002): 475–81. http://dx.doi.org/10.1016/s0022-247x(02)00231-7.

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24

Palmer, Kenneth J., Sergei Yu Pilyugin, and Sergey B. Tikhomirov. "Lipschitz shadowing and structural stability of flows." Journal of Differential Equations 252, no. 2 (2012): 1723–47. http://dx.doi.org/10.1016/j.jde.2011.07.026.

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25

Stepanov, A. V. "Generalizations in the problem of Lipschitz stability." Journal of Mathematical Sciences 90, no. 6 (1998): 2524–26. http://dx.doi.org/10.1007/bf02433001.

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26

Alessandrini, Giovanni, and Sergio Vessella. "Lipschitz stability for the inverse conductivity problem." Advances in Applied Mathematics 35, no. 2 (2005): 207–41. http://dx.doi.org/10.1016/j.aam.2004.12.002.

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27

Bainov, D. D., and I. M. Stamova. "Lipschitz stability of impulsive functional-differential equations." ANZIAM Journal 42, no. 4 (2001): 504–14. http://dx.doi.org/10.1017/s1446181100012244.

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AbstractAn initial value problem is considered for impulsive functional-differential equations. The impulses occur at fixed moments of time. Sufficient conditions are found for Lipschitz stability of the zero solution of these equations. An application in impulsive population dynamics is also discussed.

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28

Choi, Sang Il, and Yoon Hoe Goo. "LIPSCHITZ STABILITY FOR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS." Far East Journal of Mathematical Sciences (FJMS) 96, no. 5 (2015): 573–91. http://dx.doi.org/10.17654/fjmsmar2015_573_591.

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29

Choi, Sang Il, and Yoon Hoe Goo. "UNIFORM LIPSCHITZ STABILITY OF PERTURBED DIFFERENTIAL SYSTEMS." Far East Journal of Mathematical Sciences (FJMS) 101, no. 4 (2017): 721–35. http://dx.doi.org/10.17654/ms101040721.

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30

Elaydi, S., and M. Rama Mohana Rao. "Lipschitz stability for nonlinear volterra integrodifferential systems." Applied Mathematics and Computation 27, no. 3 (1988): 191–99. http://dx.doi.org/10.1016/0096-3003(88)90001-x.

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31

Pinsky, Mark A., and Steve Koblik. "Solution Bounds, Stability, and Estimation of Trapping/Stability Regions of Some Nonlinear Time-Varying Systems." Mathematical Problems in Engineering 2020 (April 24, 2020): 1–16. http://dx.doi.org/10.1155/2020/5128430.

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Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science, and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which bounds the solution norms, derives the corresponding stability criteria, and estimates the trapping/stability regions for some nonautonomous and nonlinear systems, which arise in various application domains. Our inferences rest on deriving a scalar differential inequality for the norms of solutions to the initial systems. Utility of the Li

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32

Kamalapurkar, Rushikesh, Warren E. Dixon, and Andrew R. Teel. "On reduction of differential inclusions and Lyapunov stability." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 24. http://dx.doi.org/10.1051/cocv/2019074.

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In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is pointwise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative sta

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33

Zhang, Liwei, Shengzhe Gao, and Saoyan Guo. "Statistical Inference of Second-Order Cone Programming." Asia-Pacific Journal of Operational Research 36, no. 02 (2019): 1940003. http://dx.doi.org/10.1142/s0217595919400037.

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In this paper, we study the stability of stochastic second-order programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are demonstrated. Moreover, we prove that, if the constraint non-degeneracy condition and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush–Kuhn–Tucker

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34

Araujo, Alexandre, Benjamin Negrevergne, Yann Chevaleyre, and Jamal Atif. "On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 6661–69. http://dx.doi.org/10.1609/aaai.v35i8.16824.

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This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks. Lipschitz regularity is now established as a key property of modern deep learning with implications in training stability, generalization, robustness against adversarial examples, etc. However, computing the exact value of the Lipschitz constant of a neural network is known to be NP-hard. Recent attempts from the literature introduce upper bounds to approximate this constant that are either efficient but loose or accurate but computationally expensive. In this work, by leveraging the theory of Toeplitz

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35

Foschiatti, Sonia, Romina Gaburro, and Eva Sincich. "Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad hoc misfit functional." Inverse Problems 37, no. 12 (2021): 125007. http://dx.doi.org/10.1088/1361-6420/ac349c.

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Abstract We address the stability issue in Calderón’s problem for a special class of anisotropic conductivities of the form σ = γA in a Lipschitz domain Ω ⊂ R n , n ⩾ 3, where A is a known Lipschitz continuous matrix-valued function and γ is the unknown piecewise affine scalar function on a given partition of Ω. We define an ad hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.

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36

Chen, Kun-Chu. "Stability estimate for a strongly coupled parabolic system." Tamkang Journal of Mathematics 43, no. 1 (2012): 137–44. http://dx.doi.org/10.5556/j.tkjm.43.2012.897.

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37

Liu, Kanglin, and Guoping Qiu. "Lipschitz constrained GANs via boundedness and continuity." Neural Computing and Applications 32, no. 24 (2020): 18271–83. http://dx.doi.org/10.1007/s00521-020-04954-z.

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AbstractOne of the challenges in the study of generative adversarial networks (GANs) is the difficulty of its performance control. Lipschitz constraint is essential in guaranteeing training stability for GANs. Although heuristic methods such as weight clipping, gradient penalty and spectral normalization have been proposed to enforce Lipschitz constraint, it is still difficult to achieve a solution that is both practically effective and theoretically provably satisfying a Lipschitz constraint. In this paper, we introduce the boundedness and continuity (BC) conditions to enforce the Lipschitz c

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38

Lee, Keon-Hee. "Recurrence in Lipschitz stable flows." Bulletin of the Australian Mathematical Society 38, no. 2 (1988): 197–202. http://dx.doi.org/10.1017/s0004972700027465.

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The purpose of this paper is to get some necessary conditions for a Poisson stable flow to be recurrent and to analyse the bilateral versions of positive and negative Lipschitz stability. Moreover, a characterisation of recurrent orbits is obtained in a certain flow.

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39

Wang, Xue, Danfeng Luo, Zhiguo Luo, and Akbar Zada. "Ulam–Hyers Stability of Caputo-Type Fractional Stochastic Differential Equations with Time Delays." Mathematical Problems in Engineering 2021 (March 29, 2021): 1–24. http://dx.doi.org/10.1155/2021/5599206.

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In this paper, we study a class of Caputo-type fractional stochastic differential equations (FSDEs) with time delays. Under some new criteria, we get the existence and uniqueness of solutions to FSDEs by Carath e ´ odory approximation. Furthermore, with the help of H o ¨ lder’s inequality, Jensen’s inequality, It o ^ isometry, and Gronwall’s inequality, the Ulam–Hyers stability of the considered system is investigated by using Lipschitz condition and non-Lipschitz condition, respectively. As an application, we give two representative examples to show the validity of our theories.

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40

Barreira, Luis, and Claudia Valls. "Stability of delay equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 45 (2022): 1–24. http://dx.doi.org/10.14232/ejqtde.2022.1.45.

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For a large class of nonautonomous linear delay equations with distributed delay, we obtain the equivalence of hyperbolicity, with the existence of an exponential dichotomy, and Ulam–Hyers stability. In particular, for linear equations with constant or periodic coefficients and with a simple spectrum these two properties are equivalent. We also show that any linear delay equation with an exponential dichotomy and its sufficiently small Lipschitz perturbations are Ulam–Hyers stable.

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41

Zhang, Gui-Lai, Zhi-Yong Zhu, Yu-Chen Wang, and Chao Liu. "Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses." Mathematics 12, no. 19 (2024): 3002. http://dx.doi.org/10.3390/math12193002.

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In this paper, we study the asymptotical stability of the exact solutions of nonlinear impulsive differential equations with the Lipschitz continuous function f(t,x) for the dynamic system and for the impulsive term Lipschitz continuous delayed functions Ik. In order to obtain numerical methods with a high order of convergence and that are capable of preserving the asymptotical stability of the exact solutions of these equations, impulsive discrete Runge–Kutta methods and impulsive continuous Runge–Kutta methods are constructed, respectively. For these different types of numerical methods, dif

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42

Djordjevic, Jasmina. "Lp - estimates of solutions of backward doubly stochastic differential equations." Filomat 31, no. 8 (2017): 2365–79. http://dx.doi.org/10.2298/fil1708365d.

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This paper deals with a large class of nonhomogeneous backward doubly stochastic differential equations which have a more general form of the forward It? integrals. Terms under which the solutions of these equations are bounded in the Lp-sense, p ? 2, under both the Lipschitz and non-Lipschitz conditions, are given, i.e. Lp - stability for this general type of backward doubly stochastic differential equations is established.

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43

Wang, Mei, and Baogua Jia. "Finite-time stability and uniqueness theorem of solutions of nabla fractional $ (q, h) $-difference equations with non-Lipschitz and nonlinear conditions." AIMS Mathematics 9, no. 6 (2024): 15132–48. http://dx.doi.org/10.3934/math.2024734.

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<abstract><p>In this paper, the discrete $ (q, h) $-fractional Bihari inequality is generalized. On the grounds of inequality, the finite-time stability and uniqueness theorem of solutions of $ (q, h) $-fractional difference equations with non-Lipschitz and nonlinear conditions is concluded. In addition, the validity of our conclusion is illustrated by a nonlinear example with a non-Lipschitz condition.</p></abstract>

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44

Reinfelds, Andrejs, and Shraddha Christian. "Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales." Mathematics 12, no. 9 (2024): 1379. http://dx.doi.org/10.3390/math12091379.

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In this paper, we present sufficient conditions for Hyers–Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.

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45

Chahbi, Abdellatif, Iz-iddine EL-Fassi, and Samir Kabbaj. "Lipschitz stability of the k-quadratic functional equation." Quaestiones Mathematicae 40, no. 8 (2017): 991–1001. http://dx.doi.org/10.2989/16073606.2017.1339742.

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46

Rondi, Luca. "Optimal Stability of Reconstruction of Plane Lipschitz Cracks." SIAM Journal on Mathematical Analysis 36, no. 4 (2005): 1282–92. http://dx.doi.org/10.1137/s0036141003435837.

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47

Alessandrini, Giovanni, Elena Beretta, and Sergio Vessella. "Determining Linear Cracks by Boundary Measurements: Lipschitz Stability." SIAM Journal on Mathematical Analysis 27, no. 2 (1996): 361–75. http://dx.doi.org/10.1137/s0036141094265791.

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48

Kulev, G. K., and D. D. Bainov. "Lipschitz stability of impulsive systems of differential equations." Dynamics and Stability of Systems 8, no. 1 (1993): 1–17. http://dx.doi.org/10.1080/02681119308806145.

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49

Dishliev, A. B., and D. D. Bainov. "Investigation of the lipschitz stability via limiting equations." Dynamics and Stability of Systems 5, no. 2 (1990): 59–64. http://dx.doi.org/10.1080/02681119008806085.

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50

Tabor, Jacek. "Lipschitz Stability of the Cauchy and Jensen Equations." Results in Mathematics 32, no. 1-2 (1997): 133–44. http://dx.doi.org/10.1007/bf03322533.

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