The oscillation of separately locally Lipschitz functions
Karpatsʹkì Matematičnì Publìkacìï, 2013 We prove that a function which dened on the product of two metric Baire spaces is the oscillation of some separately locally Lipschitz function if and only if it is an upper semicontinuous non-negative function which has a crosswise nowhere dense closure
V. H. Herasymchuk, O. V. Maslyuchenko
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Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations [PDF]
, 2007 Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability.
Yuan, C. +4 more
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Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains [PDF]
, 2002 Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of ...
M. Mitrea +3 more
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Distributed convex optimization via proportional-integral-differential algorithm
Measurement + Control, 2022 This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents.
Wei Zhu, Haibao Tian
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Existence of fixed points on compact epilipschitz sets without invariance conditions
Fixed Point Theory and Applications, 2005 We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set).
Marc Quincampoix, Mikhail Kamenskii
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Discretization methods for nonconvex differential inclusions
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We prove the existence of solutions for the differential inclusion $\dot x(t)\in F(t,x(t)) + f(t,x(t))$ for a multifunction $F$ upper semicontinuous with compact values contained in the generalized Clarke gradient of a regular locally Lipschitz function ...
M. Yarou
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Some notes on commutators of the fractional maximal function on variable Lebesgue spaces
Journal of Inequalities and Applications, 2019 Let ...
Pu Zhang, Zengyan Si, Jianglong Wu
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On compactness and connectedness of the paratingent [PDF]
, 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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A Multiplicity Theorem for Locally Lipschitz Periodic Functionals
Journal of Mathematical Analysis and Applications, 1995 The authors consider the periodic multivalued problem of the forced pendulum \[ \begin{cases} x''(t) + f(t)\in \biggl[\underline g\bigl(x(t) \bigr), \overline g \bigl(x(t) \bigr)\biggr], \quad \text{a.e. } t\in(0,1) \\ x(0) = x(1),\;x'(0) = x'(1) \end{cases} \] where \(f\in L^p(0,1)\), \(g\in L^\infty (\mathbb{R})\) is periodic of period \(T\), the ...
Mironescu, P., Radulescu, V.D.
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Some Inexact Version of the Iterative Exponential Method for Solving Nonsmooth Equations
Algorithms, 2023 This paper presents an inexact version of an exponential iterative method designed for solving nonlinear equations F(x)=0, where the function F is only locally Lipschitz continuous.
Marek J. Śmietański
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