{"paper":{"title":"Existence and Properties of Semi-Bounded Global Solutions to the Functional Differential Equation with Volterra's Type Operators on the Real Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Maitere Aguerrea, Robert Hakl","submitted_at":"2015-07-30T16:32:54Z","abstract_excerpt":"Consider the equation $$ u'(t)=\\ell_0(u)(t)-\\ell_1(u)(t)+f(u)(t)\\qquad\\mbox{for~a.~e.~}\\,t\\in\\mathbb{R} $$ where $\\ell_i:C_{loc}\\big(\\mathbb{R};\\mathbb{R}\\big)\\to L_{loc}\\big(\\mathbb{R};\\mathbb{R}\\big)$ $(i=0,1)$ are linear positive continuous operators and $f:C_{loc}\\big(\\mathbb{R};\\mathbb{R}\\big)\\to L_{loc}\\big(\\mathbb{R};\\mathbb{R}\\big)$ is a continuous operator satisfying the local Carath\\'eodory conditions. The efficient conditions guaranteeing the existence of a global solution, which is bounded and non-negative in the neighbourhood of $-\\infty$, to the equation considered are establishe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08573","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"}