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We suppose that $g:\\mathbb{R}^{n}\\rightarrow \\mathbb{R}^{n}$ is an odd continuous function that satisfies $g(0)=g^{\\prime }(0)=0$ and the Nagumo condition. Assuming that the graph is invariant by a subgroup of permutations $\\Gamma$, using a $\\Gamma$-equivariant topological invariant we prove the existence of multiple non-constant $p$-periodic solutions characterized by their symmetries."},"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":"1804.10803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-28T13:45:04Z","cross_cats_sorted":[],"title_canon_sha256":"2e7d1f3585c38ffa90879e1a0b5a9e2b79e8283699c50100fe86083e294965ae","abstract_canon_sha256":"bd445a6387e8566b0c7ed33b12efa730a4216b69b4018990a7271d949de91c08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:15.508002Z","signature_b64":"Ynofl3Z8GawSCsAWa1cvqTOAhB61rvXr9gaJ2y06VWlm/m4STq16miJpgYU8ChJCZcQgnhd/86MUw7eqU5y5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e0d906aefacc56ca0e72c15d83d799178964cbcaad52636beab1b4670f8750","last_reissued_at":"2026-05-18T00:17:15.507357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:15.507357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions of Fixed Period in the Nonlinear Wave Equation on Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Garc\\'ia-Azpeitia, Wieslaw Krawcewicz, Yanli Lv","submitted_at":"2018-04-28T13:45:04Z","abstract_excerpt":"The wave equation on network is defined by $\\partial_{tt}u=\\Delta_{G}u+g(u)$, where $u\\in\\mathbb{R}^{n}$ and the graph Laplacian $\\Delta_{G}$ is an operator on functions on $n$ vertices. 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