{"paper":{"title":"Existence of positive solutions for an approximation of stationary mean-field games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreia Chapouto, Andr\\'e Rodrigues, Avetik Karagulyan, Chuliang Song, Daniela Jord\\~ao, David Evangelista Junior, Diogo Gomes, Elena Bachini, Giorgia Pagliar, Hector Velasco-Perez, Jo\\~ao Reis, Juan Monasterio, Kengo Terai, Levon Nurbekyan, Marco Piccirilli, Mariana Prazeres, Maria Sargsyan, Nojood Almayouf, Orlando Romero, Rita Ferreira, Ryota Tomisaki, Sagar Pratapsi, Tommaso Seneci, Vardan Voskanyan, Xianjin Yang","submitted_at":"2015-11-22T12:01:09Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06999","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}