A nonsmooth principle of symmetric criticality and variational–hemivariational inequalities

AbstractIn the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.

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Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

Advances in Difference Equations ◽

10.1186/s13662-021-03373-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

M. Mohan Raja ◽

V. Vijayakumar ◽

Le Nhat Huynh ◽

R. Udhayakumar ◽

Kottakkaran Sooppy Nisar

Keyword(s):

Fixed Point ◽

Control Systems ◽

Approximate Controllability ◽

Hemivariational Inequalities ◽

Evolution Inclusions ◽

Fractional Systems ◽

Cosine Families ◽

Fixed Point Approach ◽

Semilinear Control Systems ◽

Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

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Vanishing viscosity for hemivariational inequalities modeling dynamic problems in elasticity

Nonlinear Analysis ◽

10.1016/j.na.2006.02.028 ◽

2007 ◽

Vol 66 (8) ◽

pp. 1840-1852 ◽

Cited By ~ 14

Author(s):

Stanisław Migórski ◽

Anna Ochal

Keyword(s):

Hemivariational Inequalities ◽

Dynamic Problems ◽

Vanishing Viscosity

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ON EIGENVALUE PROBLEMS FOR ELLIPTIC HEMIVARIATIONAL INEQUALITIES

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091506001246 ◽

2008 ◽

Vol 51 (2) ◽

pp. 407-419 ◽

Cited By ~ 4

Author(s):

Zhenhai Liu ◽

Guifang Liu

Keyword(s):

Dirichlet Problem ◽

Eigenvalue Problems ◽

Hemivariational Inequalities ◽

Generalized Gradient ◽

At Resonance ◽

Quasilinear Elliptic ◽

First Eigenfunction

AbstractThis paper is devoted to the Dirichlet problem for quasilinear elliptic hemivariational inequalities at resonance as well as at non-resonance. Using Clarke's notion of the generalized gradient and the property of the first eigenfunction, we also build a Landesman–Lazer theory in the non-smooth framework of quasilinear elliptic hemivariational inequalities.

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