Existence of positive solutions for an approximation of stationary mean-field games

  title={Existence of positive solutions for an approximation of stationary mean-field games},
  author={Nojood Almayouf and Elena Bachini and Andreia Chapouto and R. Ferreira and Diogo Gomes and D. Jord{\~a}o and David Evangelista Junior and Avetik G. Karagulyan and J. Monasterio and L. Nurbekyan and Giorgia Pagliar and Marco Piccirilli and S. Pratapsi and M. Prazeres and J. Reis and Andre Rodrigues and Orlando Romero and M. Sargsyan and Tommaso Seneci and C. Song and Kengo Terai and Ryota Tomisaki and H. Velasco-Perez and Vardan K. Voskanyan and Xianjin Yang},
  journal={Involve, A Journal of Mathematics},
  • Nojood Almayouf, Elena Bachini, +22 authors Xianjin Yang
  • Published 2017
  • Mathematics
  • Involve, A Journal of Mathematics
  • Here, we consider a regularized mean-field game model that features a low-order regularization. We prove the existence of solutions with positive density. To do so, we combine a priori estimates with the continuation method. In contrast with high-order regularizations, the low-order regularizations are easier to implement numerically. Moreover, our methods give a theoretical foundation for this approach. 
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