{"paper":{"title":"Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan-Song Zhou, Xiaoyu Zeng, Yujin Guo, Zhi-qiang Wang","submitted_at":"2015-02-06T10:12:50Z","abstract_excerpt":"We are interested in the attractive Gross-Pitaevskii (GP) equation in $\\R^2$, where the external potential $V(x)$ vanishes on $m$ disjoint bounded domains $\\Omega_i\\subset \\R^2\\ (i=1,2,\\cdots,m)$ and $V(x)\\to\\infty$ as $|x|\\to\\infty$, that is, the union of these $\\Omega_i$ is the bottom of the potential well. By making some delicate estimates on the energy functional of the GP equation, we prove that when the interaction strength $a$ approaches some critical value $a^*$ the ground states concentrate and blow up at the center of the incircle of some $\\Omega_j$ which has the largest inradius. Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01839","kind":"arxiv","version":1},"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"}