Advances in Variational and Hemivariational Inequalities

We consider a nonlinear Dirichlet parametric problem with discontinuous right hand side in which we have a competing effect of sub and superlinear nonlinearities. A bifurcation type result is studied when the parameter tends to zero.

[1]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[2]  J. T. Oden,et al.  Models and computational methods for dynamic friction phenomena , 1984 .

[3]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[4]  T. Q. Bao,et al.  A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities , 2005 .

[5]  Yiran He,et al.  An algorithm for generalized variational inequality with pseudomonotone mapping , 2009 .

[6]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[7]  R. Rockafellar.  Monotone Operators and the Proximal Point Algorithm , 1976 .

[8]  Felix Schlenk,et al.  Proof of Theorem 3 , 2005 .

[9]  Yiran He,et al.  A double projection algorithm for multi-valued variational inequalities and a unified framework of the method , 2011, Appl. Math. Comput..

[10]  C. Baiocchi,et al.  Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .

[11]  J. Rodriguez,et al.  Problem (2) , 1994 .

[12]  Chunde Yang,et al.  An algorithm for solving a multi-valued variational inequality , 2013, Journal of Inequalities and Applications.

[13]  Majid Fakhar,et al.  On generalized variational inequalities , 2009, J. Glob. Optim..

[14]  Nan-Jing Huang,et al.  A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities , 2011, J. Optim. Theory Appl..

[15]  W. Marsden.  I and J , 2012 .

[16]  M. Solodov,et al.  A New Projection Method for Variational Inequality Problems , 1999 .

[17]  Yiran He.  A new double projection algorithm for variational inequalities , 2006 .

[18]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[19]  Marc Teboulle,et al.  Lagrangian Duality and Related Multiplier Methods for Variational Inequality Problems , 1999, SIAM J. Optim..

[20]  Anna Nagurney,et al.  Variational Inequalities , 2009, Encyclopedia of Optimization.

[21]  H. Attouch.  Variational convergence for functions and operators , 1984 .

[23]  Romesh Saigal,et al.  Extension of the Generalized Complementarity Problem , 1976, Math. Oper. Res..

[24]  J. C. Simo,et al.  The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics , 1992 .

[25]  Elisabetta Allevi,et al.  The Proximal Point Method for Nonmonotone Variational Inequalities , 2006, Math. Methods Oper. Res..

[26]  I. Konnov.  Combined Relaxation Methods for Variational Inequalities , 2000 .

[27]  M. Sofonea,et al.  Two History-Dependent Contact Problems , 2015 .

[28]  Muhammad Aslam Noor,et al.  Hemivariational inequalities , 2005 .

[29]  Masao Fukushima,et al.  The primal douglas-rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem , 1996, Math. Program..

[30]  Changjie Fang,et al.  A Projection-Type Method for Multivalued Variational Inequality , 2013 .

[31]  L. Véron,et al.  Quasilinear elliptic equations involving critical Sobolev exponents , 1989 .

[32]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[33]  Abdellah Bnouhachem.  A self-adaptive method for solving general mixed variational inequalities , 2005 .

[34]  Z. Luo.  A Class of Iterative Methods for Solving Nonlinear Projection Equations , 2005 .

[35]  G. Łukaszewicz,et al.  On Large Time Asymptotics for Two Classes of Contact Problems , 2015 .

[36]  R. Shivaji,et al.  Multiple positive solutions for a class of semilinear elliptic boundary value problems , 1999 .

[37]  Christiane Tammer,et al.  Proximal Methods for the Elastography Inverse Problem of Tumor Identification Using an Equation Error Approach , 2015 .

[38]  J. Moreau.  On Unilateral Constraints, Friction and Plasticity , 2011 .

[39]  Jean-Jacques Strodiot,et al.  A Bundle Method for Solving Variational Inequalities , 2004, SIAM J. Optim..

[40]  Yair Censor,et al.  The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space , 2011, J. Optim. Theory Appl..

[41]  Jaroslav Haslinger,et al.  Finite Element Method for Hemivariational Inequalities , 1999 .

[42]  M. Sofonea,et al.  Nonlinear Inclusions and Hemivariational Inequalities , 2013 .

[43]  S. Karamardian.  Complementarity problems over cones with monotone and pseudomonotone maps , 1976 .

[44]  G. Stampacchia,et al.  On some non-linear elliptic differential-functional equations , 1966 .

[45]  F. Clarke.  Generalized gradients and applications , 1975 .

[46]  D. Goeleven,et al.  A Non-clamped Frictional Contact Problem with Normal Compliance , 2015 .

[47]  Hemivariational Inequalities for Dynamic Elastic-Viscoplastic Contact Problems , 2015 .

[48]  Naihua Xiu,et al.  Modified Extragradient Method for Variational Inequalities and Verification of Solution Existence , 2003 .

[49]  Xiang-Sun Zhang,et al.  Modified fixed-point equations and related iterative methods for variational inequalities , 2004 .

[50]  P. D. Panagiotopoulos,et al.  Mathematical Theory of Hemivariational Inequalities and Applications , 1994 .