{"paper":{"title":"Some Remarks on Some Second-Order Elliptic Differential Equations","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Toka Diagana","submitted_at":"2003-08-14T13:23:50Z","abstract_excerpt":"We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\\ddot u(s) + 2 B \\dot u(s) + A u(s) = f(s) (\\ast),$ where $A, B$ are densely defined closed linear operators acting in a Hilbert space ${\\mathbb H}$ and $f: {\\mathbb R} \\mapsto {\\mathbb H}$ is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions; every solution to $(\\ast)$ is almost automorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0308137","kind":"arxiv","version":2},"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"}