Noncoercive mixed equilibrium problems under pseudomonotone perturbations and applications to nonlinear evolution equations with lack of coercivity

ABSTRACT

In this paper, we study the existence of solutions for noncoercive mixed equilibrium problems which are described by the sum of a maximal monotone bifunction and a pseudomonotone (or quasimonotone) bifunction in the sense of Brézis. Our approach is based on recession analysis and on recent results established by the authors for the existence of solutions of mixed equilibrium problems under pseudomonotone perturbations. As an application, we study the existence of solutions for nonlinear evolution equations associated with a noncoercive time-dependent pseudomonotone (or quasimonotone) operator.

KEYWORDS:

• Mixed equilibrium problems
• maximal monotone operators/bifunctions
• pseudomonotone operators/bifunctions in Brézis sense
• quasimonotone operators/bifunctions in topological sense
• evolution equations
• recession analysis

AMS SUBJECT CLASSIFICATIONS:

• 49J40
• 49J53
• 47J30
• 34G20

Acknowledgements

This research was done during the visit of second and third author to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Authors are grateful to KFUPM for providing excellent research facilities to carry out this work. Authors are also grateful to the referees for their valuable and useful comments and suggestions to improve the previous draft of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was funded by the KFUPM Funded Research [project number NI141030].