Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis

  • B. T. Kien
  • M. M. Wong
  • N. C. Wong
  • J. C. YaoEmail author


This paper is concerned with the study of the solution existence of variational inequalities and generalized variational inequalities in reflexive Banach spaces with pseudomonotone operators in the sense of Brézis. The obtained results cover some preceding results in Browder (J. Funct. Anal. 11:251–294, 1972), Brézis (Ann. Inst. Fourier 18:115–175, 1968), Kinderlehrer and Stampacchia (An Introduction to Variational Inequalities and Their Applications, Academic Press, San Diego, 1980), Zeidler (Nonlinear Functional Analysis and Its Applications, II/B, Springer, Berlin, 1990).


Variational inequalities Generalized variational inequalities Pseudomonotone operators Solution existence 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • B. T. Kien
    • 1
  • M. M. Wong
    • 2
  • N. C. Wong
    • 3
  • J. C. Yao
    • 3
    Email author
  1. 1.Department of Information and TechnologyHanoi University of Civil EngineeringHanoiVietnam
  2. 2.Department of Information TechnologyMeiho Institute of TechnologyPintaungTaiwan
  3. 3.Department of Applied MathematicsNational Sun Yat-Sen UniversityKaohsiungTaiwan

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