Existence results for equilibrium problems with applications to evolution equations

Abstract

In this paper, we consider evolution equations with time-dependent pseudomonotone and quasimonotone operators by a new approach based on equilibrium problems theory. We establish new existence results for equilibrium problems associated to pseudomonotone and quasimonotone bifunctions in the topological sense. The results obtained are then applied to derive existence of solutions for evolution equations. The approach is new and leads to improve and unify most of the results obtained in this direction.

Keywords:

• evolution equations
• maximal monotone operators
• pseudomonotone operators
• quasimonotone operators
• equilibrium problems
• evolution triple

AMS Subject Classifications:

• 47H05
• 49J40
• 47J20
• 47J05
• 46N20

Acknowledgements

The authors would like to thank the anonymous referee for his constructive comments, which contributed to the improvement of the present paper.

Notes

1 This work was partially supported by the NSC [grant number 103-2923-E-037-001-MY3].