Existence of Solutions for Noncoercive Hemivariational Inequalities by an Equilibrium Approach Under Pseudomonotone Perturbation

Mixed Equilibrium Problems and Anti-periodic Solutions for Nonlinear Evolution Equations

“…Consequently, by considering the upper limit in relation (12) and taking account of the demicontinuity of J , we get…”

“…The name "equilibrium problems" (in short, EP) has been given by Blum and Oettli [6], where it has been shown that equilibrium problems include variational inequalities, fixed point, Nash equilibrium and game theory as special cases. Hence, equilibrium problems have a great impact and influence in the development of several branches of pure and applied sciences, and collectively cover a vast range of applications, see for example [7][8][9][10][11][12] and for a recent survey on equilibria, see [13] and the references therein.…”

Semicoercive Variational Inequalities: From Existence to Numerical Solution of Nonmonotone Contact Problems

“…Similar reasoning based on a recession analysis can be found in [44,32,33,12,13,16,17,18,21,24]. Another approach to existence results for semicoercive pseudomonotone variational inequalities is a regularization procedure based on adding of a coercive term, see [16,19,22,28].…”

“…The existence theory of hemivariational inequalities (HVIs) and of more abstract topologically (in the sense of Brézis [10]) pseudomonotone VIs, also in the semicoercive case is well documented in the literature. Without claim of completeness we can cite [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] in chronological order While there are studies of numerical solution methods for coercive HVIs, see the book [29] of Haslinger, Miettinen, and Panagiotopoulos and also the more recent paper [30], and there are works on the numerical treatment of semicoercive monotone VIs, see the book of Kaplan and Tichatschke [31] and the papers [32,33,34,35,36,37,38], to the best of the authors' knowledge, efficient methods for the numerical solution of semicoercive HVIs supported by rigorous mathematical analysis are missing. It is the purpose of the present paper to initiate work in this direction.…”

Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

“…A great many of existence results for HVIs have been obtained when the operators involved are pseudomonotone and satisfy certain coercivity conditions [18][19][20][21][22] . However, as pointed by Liu [4] , there also are many economic, engineering, and stochastic models leading to HVIs with involved operators being non-coercive.…”