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

Abstract

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).

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Correspondence to J. C. Yao.

Additional information

Communicated by F. Giannessi.

The authors wish to thank two anonymous referees for useful suggestions and comments which improved the original manuscript greatly.

This paper was partially supported by a grant from NSC of Taiwan.

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Kien, B.T., Wong, M.M., Wong, N.C. et al. Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis. J Optim Theory Appl 140, 249–263 (2009). https://doi.org/10.1007/s10957-008-9446-7

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Keywords

  • Variational inequalities
  • Generalized variational inequalities
  • Pseudomonotone operators
  • Solution existence