{"paper":{"title":"Ground state solutions for non-autonomous fractional Choquard equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chungen Liu, Yan-Hong Chen","submitted_at":"2015-05-14T15:04:51Z","abstract_excerpt":"We consider the following nonlinear fractional Choquard equation, \\begin{equation}\\label{e:introduction} \\begin{cases} (-\\Delta)^{s} u + u = (1 + a(x))(I_\\alpha \\ast (|u|^{p}))|u|^{p - 2}u\\quad\\text{ in }\\mathbb{R}^N,\\\\ u(x)\\to 0\\quad\\text{ as }|x|\\to \\infty, \\end{cases} \\end{equation} here $s\\in (0, 1)$, $\\alpha\\in (0, N)$, $p\\in [2, \\infty)$ and $\\frac{N - 2s}{N + \\alpha} < \\frac{1}{p} < \\frac{N}{N + \\alpha}$. Assume $\\lim_{|x|\\to\\infty}a(x) = 0$ and satisfying suitable assumptions but not requiring any symmetry property on $a(x)$, we prove the existence of ground state solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03749","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"}