A class of impulsive differential variational inequalities in finite dimensional spaces

Li, Xuesong; Huang, Ning; O’Regan, Donal

doi:10.1016/j.jfranklin.2016.06.011

Cited by 29 publications

(17 citation statements)

References 33 publications

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“…Based on this motivation, Chen and Wang [2] in 2014 used the idea of DVIs to investigate a dynamic Nash equilibrium problem of multiple players with shared constraints and dynamic decision processes; Wang et al [3] proved an existence theorem for Carathéodory weak solutions of a differential quasi-variational inequality in finite dimensional Euclidean spaces and established a convergence result on the Euler time-dependent procedure for solving the initialvalue differential set-valued variational inequalities; and Migórski et al [4] used the surjectivity of setvalued pseudomonotone operators combined with a fixed point principle to prove the unique solvability of a history-dependent DVI, and then they used the abstract frameworks to study a history-dependent frictional viscoelastic contact problem with a generalized Signorini contact condition. For more details on these topics, the reader is welcome to refer to [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and references therein. More recently, Liu et al [19] initially introduced the notion of differential hemivariational inequalities (DHVIs), which is a generalization of variational inequalities.…”

Section: Introductionmentioning

confidence: 99%

On the well-posedness of differential quasi-variational-hemivariational inequalities

et al. 2020

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Abstract The goal of this paper is to discuss the well-posedness and the generalized well-posedness of a new kind of differential quasi-variational-hemivariational inequality (DQHVI) in Hilbert spaces. Employing these concepts, we explore the essential relation between metric characterizations and the well-posedness of DQHVI. Moreover, the compactness of the set of solutions for DQHVI is delivered, when problem DQHVI is well-posed in the generalized sense.

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Section: Introductionmentioning

confidence: 99%

On the well-posedness of differential quasi-variational-hemivariational inequalities

et al. 2020

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“…In 2014 Chen and Wang [8], using the idea of (DVI), have solved the dynamic Nash equilibrium problem with shared constraints, which involves a dynamic decision process with multiple players. Subsequently, Ke et al [20] in 2015 investigated a class of fractional differential variational inequalities with decay term in finite-dimensional spaces, for details on this topic in finite-dimensional spaces, we refer to [7,13,22,23,25,32,48] and the references therein. It should be pointed out that all results in the aforementioned papers were considered only in finite-dimensional spaces.…”

Section: (T)) + B(u(t)) + M * ξ(T) = F (T) For Ae T ∈ (0 T ) β (T)mentioning

confidence: 99%

“…We remark that for appropriate and suitable choices of the spaces and the above defined maps, FIDHVI includes a number of fractional differential hemivariational inequalities, impulsive differential hemivariational inequalities, fractional differential variational inequalities, impulsive differential variational inequalities, differential hemivariational inequalities, and differential variational inequalities as special cases, see for example [23,30,31,35,36,53] and the related references cited therein.…”

Section: Introductionmentioning

confidence: 99%

A class of fractional differential hemivariational inequalities with application to contact problem

Zeng

Liu

Migórski

2018

Z. Angew. Math. Phys.

106

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Abstract. In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.Mathematics Subject Classification. 35L15, 35L86, 35L87, 74Hxx, 74M10.

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“…We remark that for appropriate and suitable choices of the spaces and the above defined maps, FIDHVI includes a number of differential variational inequalities as special cases [5,12,13,26,29].…”

Section: Introductionmentioning

confidence: 99%

A new class of fractional impulsive differential hemivariational inequalities with an application

Weng

Chen

Huang

et al. 2022

NAMC

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We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result, which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.

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A class of impulsive differential variational inequalities in finite dimensional spaces

Cited by 29 publications

References 33 publications

On the well-posedness of differential quasi-variational-hemivariational inequalities

On the well-posedness of differential quasi-variational-hemivariational inequalities

A class of fractional differential hemivariational inequalities with application to contact problem

A new class of fractional impulsive differential hemivariational inequalities with an application

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