{"paper":{"title":"Variational principles for self-adjoint operator functions arising from second-order systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Birgit Jacob, Carsten Trunk, Matthias Langer","submitted_at":"2014-10-26T20:57:44Z","abstract_excerpt":"Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \\[\n  \\langle\\ddot{z}(t),y \\rangle + \\mathfrak{d}[\\dot{z} (t), y] + \\mathfrak{a}_0 [z(t),y] = 0. \\] Here $\\mathfrak{a}_0$ and $\\mathfrak{d}$ are densely defined, symmetric and positive sesquilinear forms on a Hilbert space $H$. We associate with the variational evolution equation an equivalent Cauchy problem corresponding to a block operator matrix $\\mathcal{A}$, the forms \\[\n  \\mathfrak{t}(\\lambda)[x,y] := \\lambda^2\\langle x,y\\rangle + \\lambda\\mathfrak{d}[x,y] + \\mathf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7083","kind":"arxiv","version":3},"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"}