Existence Of Solutions for The Systems of Non-Linear Hemiequilibrim Broblem

  • Ayed E. Hashoosh Department of Mathematics, University of Thi-Qar, Iraq
  • Alaa Mijd Jaber Department of Mathematics, University of Thi-Qar, Iraq
Keywords: Nonlinear hemi-equilibrium problems, Clarkes generalized gradient, locally Lipschitz functional, set-valued operator, Nonsmooth functions

Abstract

In this article, we present existence results for a general class of systems of nonlinear hemi-equilibrium  problems by using a fixed point theorem. Our parse comprises both the statuses of bounded   and    unbounded closed convex subset in real reflexive Banach space.

References

M.Alimohammady and A.E.Hashoosh,Existence theorems for α(u,v) –monotone of nonstandard hemivariaational inequality, Advances in Math.10(2) (2015) 3205-3212.

B.E. Breckner, Cs. Varga, A multiplicity result for gradient-type systems with non-differentiable term, Acta.Math.

Hungarica 118 (2008),85-104.

B.E. Breckner, A. Horvath, Cs. Varga, A multiplicity result for a special of gradient-type systems with non-differentiable term, Nonlinear Analysis T.M.A.70 (2009) ,606-620.

N. Costea, C. Varga, Systems of nonlinear hemivariational inequalities and applications, Topological Methods in

Nonlinear Analysis.1(2003) 39-67.

S. Carl, V.k. Le, D. Motreanu, Evolutionary variational-hemivariational inequalities; existence and comparison results, J. Math.Apple.345 (2008),545-558.

S. Carl and D. Motreanu, comparison for quasilinear parabolic inclusions with clarkes gradient, Adv.Nonlinear Stud.9(2009),69-80.

S. Cal and D. Motreanu, General Comparison principle for quasilinear elliptic inclusions, Nonlinear Analysis

T.M.A.70 (2009),1105-1112.

F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley (1983).

N. Costea and A. Matei, Weak solutions for nonlinear antiplane problems leading to hemivariational inequalities

Nonlinear Analysis T.M.A.72 (2010),3669-3680.

N.Costea and V.Radulescu, Existence results for hemivariational inequalities involving relaxed η-α monotone mappings,Commum.Appl.Anal.13(2009),293-304.

N. Costea, Existence and uniqueness results for a class of quasi-hemivariational inequalities, J. Math.Anal. Appl,373 (1) (2011),305-311.

A. Eva Molnar and Orsolya Vas, An existence result for nonlinear hemivaraiational-like inequality systems, Stud.Univ. Babes-Bolyai Math.58(2013), No.3,381-392

G Fichera, Problemi electrostatici con vincoli unilaterali:il problema de Signorini con ambigue condizioni al

Contorno, Mem.Acad. Naz.Lincei,7(1964),91-140.

D. Goeleven, D. Motreanu, Y. Dumont, and M. Rochdi, Variational and Hemivariational Inequalities, Theory, MethodsBoston/London, (2003).

A.E.Hashoosh ,M.Alimohammady and M.K.Kalleji.Existence Results for Some Equilibrium Problems involving α-Monotone Bifunction,International Journal of Mathemtics and Mathemtical Sciences,(2016) 1-5.

A.E. Hashoosh and M. Alimohammady, and G.A. Almusawi, Existence Results for Nonlinear Quasi-hemivariational Inequality Systems, Journal of Thi-Qar University, Vol.11 No.4 (2016).

A.E. Hashoosh and M. Alimohammady, Existence and uniqueness results for a nonstandard variation-hemivariational inequalities with application, Int.J. Industrial Mathematics (2016), accepted.

P. Hartman, G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math.,115(1966),271-310.

Kristaly, An existence result for gradient-type systems with a nondifferentiable term on unbounded strips, J.Math.Anal.Appl.229 (2004),186-204.

A. Kristaly, V. Radulescu and Cs. Varge, Variational Principles in Mathematical physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral problems, Encyclopedia of Mathematics(No.136), Cambridge University Press, Cambridge, (2010).

T.C. Lin, Convex sets, fixed points, variational and minimax inequalities, Ball.Austral.Math.Soc.34(1986),107-117.

J.L. Lions, Stampacchia, G., Variational inequalities, Comm.Pure Appl.Math.,20(1967),493-519.

S. Migorski, a class of hemivariational inequalities for electroelastic contact problems with slip dependent friction, Discrete and Continuous Dynamical Systems Series S 1(1) (2008), 117-126.

D. Moteanu and P.D. Panagiotopoulos, Minimax Theorems and Qualitative Properties of the Solutions of Hemi-

Variational Inequalitaties and Application, Kluwer Academic Publishers, Nonconvex Optimization and its Applications, vol.29, Boston/Dordrecht/London, (1999).

D. Motreanu and V. Radulescu, Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value problems, Kluwer A cademic Publishers, Boston/Dordrecht/London, (2003).

Z. Naniewicz and P.D. Panagiotopoulos, Mathematical Theory of Hemivariational Inequalities and Applications,

Marcel, Dekker, New York, (1995).

P.D. Panagiotopoulos, Nonconvex energy functions Hemivariational inequalities and substationarity principle,

Acta Mechanica 42(1983),160-183.

P.D. Panagiotopoulos, Inequality Problems in Mechanics and Applications.Convex and Nonconvex Energy Functions, Birkhauser, Basel, (1985).

P.D. Panagiotopoulous, Hemivariational Inequalities: Applications to Mechanics and Engineering, Springer-Verlag, New York/Boston/Berlin, (1993).

Published
2021-02-18
Section
Articles