{"paper":{"title":"Nonlocal scalar field equations: qualitative properties, asymptotic profiles and local uniqueness of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debangana Mukherjee, Mousomi Bhakta","submitted_at":"2018-03-12T02:28:45Z","abstract_excerpt":"We study the nonlocal scalar field equation with a vanishing parameter \\[ \\left\\{\\begin{array}{lll}\n  (-\\Delta)^s u+\\epsilon u &=|u|^{p-2}u -|u|^{q-2}u \\quad\\text{in}\\quad\\mathbb{R}^N \\\\ u >0, & u \\in H^s(\\mathbb{R}^N),\n  \\end{array}\n  \\right. \\] where $s\\in(0,1)$, $N>2s$, $q>p>2$ are fixed parameters and $\\epsilon>0$ is a vanishing parameter. For $\\epsilon>0$ small, we prove the existence of a ground state solution and show that any positive solution of above problem is a classical solution and radially symmetric and symmetric decreasing. We also obtain the decay rate of solution at infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04093","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"}