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We consider the situation where the equation is at resonance at infinity, which means that $\\lambda$ is an eigenvalue of $A$ and $F$ is a bounded map. We introduce new geometrical conditions for the nonlinearity $F$ and use topological degree methods to find $T$-periodic solutions for this equation as fixed points of Poincar\\'e operator."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.6794","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-25T00:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"da9f47f96fdba1f0600478efd20420e7e448835b059014d8a4d0332a1f9dba88","abstract_canon_sha256":"a8e46cfa5f7e26c44378aa96a0b6ef6b511a0f49261943fc9b41029d63175b6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:26.244541Z","signature_b64":"SfjVejfRxVWH9DQ/EtUgv+FZ/gMhEb1vlOXRAeoFATq/txD2mZ7Wj17+ihamsFOmgv3gnTo2fWtim3vDH2nOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d34b5d6a19d89eb94df558b6e8e5d44d3497155ebfe037e7f50bd4f32c97bfd","last_reissued_at":"2026-05-18T01:28:26.243679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:26.243679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Effect of resonance on the existence of periodic solutions for strongly damped wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Piotr Kokocki","submitted_at":"2013-10-25T00:39:08Z","abstract_excerpt":"We are interested in the differential equation $\\ddot u(t) = -A u(t) - c A \\dot u(t) + \\lambda u(t) + F(t,u(t))$, where $c > 0$ is a damping factor, $A$ is a sectorial operator and $F$ is a continuous map. We consider the situation where the equation is at resonance at infinity, which means that $\\lambda$ is an eigenvalue of $A$ and $F$ is a bounded map. 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