Existence of Solutions for a Class of Noncoercive Variational–Hemivariational Inequalities Arising in Contact Problems

Liu, Yongjian; Liu, Zhenhai; Wen, Ching‐Feng; Yao, Jen‐Chih; Zeng, Shengda

doi:10.1007/s00245-020-09703-1

Cited by 30 publications

(9 citation statements)

References 36 publications

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“…) ⊂ E * is coercive as well. Therefore, we can invoke the same arguments as in the proof of [3,Theorem 3] to conclude that the solution set of inequality problem (1.1) (resp. ( Step 3.…”

Section: Andmentioning

confidence: 94%

“…The variational-hemivariational inequalities of form (1.9) were studied from various perspectives. For example, the results on noncoercive hemivariational inequalities can be found in [2] where the equilibrium problems were employed, and in [3] where an application to contact problems in mechanics were treated. Several classes of variational-hemivariational and hemivariational inequalities that model the problems in contact mechanics were also studied in [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Existence of solutions to a new class of coupled variational-hemivariational inequalities

2022

J. Nonlinear Var. Anal.

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The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We establish the nonemptiness and compactness of the solution set to the system. We apply a new proof based on a multivalued version of the Tychonoff fixed point principle in a Banach space combined with the generalized monotonicity arguments, and the elements of the nonsmooth analysis. Our results improve and generalize some earlier theorems obtained for a particular form of the system.

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“…) ⊂ E * is coercive as well. Therefore, we can invoke the same arguments as in the proof of [3,Theorem 3] to conclude that the solution set of inequality problem (1.1) (resp. ( Step 3.…”

Section: Andmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Existence of solutions to a new class of coupled variational-hemivariational inequalities

2022

J. Nonlinear Var. Anal.

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“…The following theorem provides a useful criterion to determinate the existence of solutions for a class of mixed variational inequalities involving pseudomonotone operators, see, for example, Liu-Liu-Wen-Yao-Zeng [31,Proposition 5].…”

Section: Preliminariesmentioning

confidence: 99%

Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions

Zeng¹,

Rădulescu²,

Winkert³

2021

Preprint

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In this paper we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), three multivalued terms and an implicit obstacle constraint. Under very general assumptions on the data, we prove that the solution set of such implicit obstacle problem is nonempty (so there is at least one solution) and weakly compact. The proof of our main result uses the Kakutani-Ky Fan fixed point theorem for multivalued operators along with the theory of nonsmooth analysis and variational methods for pseudomonotone operators.

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“…The existence of solutions to various classes of these problems is studied in Liu et al (2021, 2020, 2022b, 2019). Moreover, in some cases of the mentioned problems, often in applications, it is not possible to find a solution for OCPs in analytical form.…”

Section: Introductionmentioning

confidence: 99%

Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method

Sabermahani

Ordokhani

2023

Journal of Vibration and Control

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A new approach to finding the approximate solution of distributed-order fractional optimal control problems (D-O FOCPs) is proposed. This method is based on Fibonacci wavelets (FWs). We present a new Riemann–Liouville operational matrix for FWs using the hypergeometric function. Using this, an operational matrix of the distributed-order fractional derivative is presented. Implementing the mentioned operational matrix with the help of the Gauss–Legendre numerical integration, the problem converts to a system of algebraic equations. Error analysis is proposed. Finally, the validation of the present technique is checked by solving some numerical examples.

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Existence of Solutions for a Class of Noncoercive Variational–Hemivariational Inequalities Arising in Contact Problems

Cited by 30 publications

References 36 publications

Existence of solutions to a new class of coupled variational-hemivariational inequalities

Existence of solutions to a new class of coupled variational-hemivariational inequalities

Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions

Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method

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