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This allows  to improve some results on uniqueness and asymptotic stability of periodic or almost periodic solutions of the equation$$ u''+ cu' + g(u)=f(t) $$where $c>0$,  $f \\in L^\\infty (R)$  and $g\\in C^1(R)$ satisfies some sign hypotheses. The typical case is $ g(u) = bu + a\\vert u\\vert^p u $ with $a\\ge 0 , b>0.$ Similar properties are valid for evolution equations of the form $$ u''+ cu' + (B+A("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.01298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-04T09:40:23Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"4ddc63b8081fb8b68d0a829fd65775536b7b163440403a9f27c990215e79294f","abstract_canon_sha256":"fec549cf3e38b513b47c02bcb645941282d5384bc516e06fc72a25dc3736ee7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:17.087957Z","signature_b64":"t1qQCcMgcAbXKExCy8FJCJgImd9W44KXRyxcVWAYLEZozIg9d7d77qCMv0c/GPAmTx9pSk3Xa86qOIW/WeqfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cab5368ca1589924f819a9626c27106fe22dcd689543994a4d3a06ea2b3329b2","last_reissued_at":"2026-05-17T23:44:17.087406Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:17.087406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp stability criterion for single well Duffing and Duffing-like equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DS","authors_text":"Alain Haraux (LJLL)","submitted_at":"2019-06-04T09:40:23Z","abstract_excerpt":"We refine some previous sufficient conditions for exponential stability of the linear ODE  $$ u''+ cu' + (b+a(t))u = 0$$ where $b, c>0$ and $a$ is a bounded nonnegative time dependent coefficient. This allows  to improve some results on uniqueness and asymptotic stability of periodic or almost periodic solutions of the equation$$ u''+ cu' + g(u)=f(t) $$where $c>0$,  $f \\in L^\\infty (R)$  and $g\\in C^1(R)$ satisfies some sign hypotheses. 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