{"paper":{"title":"On the solvability of resonance problems for nonlocal elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sarika Goyal","submitted_at":"2016-07-26T08:28:23Z","abstract_excerpt":"In this article, we consider the following problem: $$ \\quad \\left\\{ \\begin{array}{lr} \\quad (-\\Delta)^s u = \\alpha u^+ -\\beta u^{-} + f(u) + h \\; \\text{in}\\;\\Omega \\quad \\quad \\quad \\quad u =0 \\; \\text{on}\\; \\mathbb{R}^n\\setminus \\Omega, \\end{array} \\right. $$ where $\\Omega\\subset \\mathbb{R}^n$ is a bounded domain with Lipschitz boundary, $n> 2s$, $0<s<1$, $(\\alpha, \\beta) \\in \\mathbb{R}^2$, $f: \\mathbb{R}\\to \\mathbb{R}$ is a bounded and continuous function and $h\\in L^2(\\Omega)$. We prove the existence results in two cases: First, the nonresonance case, where $(\\alpha,\\beta)$ is not an eleme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07584","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"}