{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NWZYDHD53ZZ3DPHEH6FOFSP7WZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"722d37bf1247d9d43eff91bfb40503b995081126f3c43d34540363a37033454a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-26T09:32:01Z","title_canon_sha256":"539f379781ae9c18e51a97c5ff980bbc52c26c26a604a94a7cfb80bea8cf3b8a"},"schema_version":"1.0","source":{"id":"1605.08206","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08206","created_at":"2026-05-18T01:02:52Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08206v2","created_at":"2026-05-18T01:02:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08206","created_at":"2026-05-18T01:02:52Z"},{"alias_kind":"pith_short_12","alias_value":"NWZYDHD53ZZ3","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NWZYDHD53ZZ3DPHE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NWZYDHD5","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:9654b4e345f5c33c83afc43b53c1bb5b63bfde146df13efef2fe10d18d8fd21d","target":"graph","created_at":"2026-05-18T01:02:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Consider the following eigenvalue problem of p-Laplacian equation \\begin{equation}\\label{P}\n  -\\Delta_{p}u+V(x)|u|^{p-2}u=\\mu|u|^{p-2}u+a| u|^{s-2}u, x\\in \\mathbb{R}^{n}, \\tag{P} \\end{equation} where $a\\geq0$, $p\\in (1,n)$ and $\\mu\\in\\mathbb{R}$. $V(x)$ is a trapping type potential, e.g., $\\inf\\limits_{x \\in \\mathbb{R}^n}V(x)< \\lim\\limits_{|x|\\rightarrow+\\infty}V(x)$. By using constrained variational methods, we proved that there is $a^*>0$, which can be given explicitly, such that problem (\\ref{P}) has a ground state $u$ with $\\|u\\|_{L^p}=1$ for some $\\mu \\in \\mathbb{R}$ and all $a\\in [0,a^*)","authors_text":"Huan-Song Zhou, Long-Jiang Gu, Xiaoyu Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-26T09:32:01Z","title":"Eigenvalue problem for a p-Laplacian equation with trapping potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08206","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa5ec28aa8ab92d4bc3f4c92d2457c93b3a6d1bad3f49b90c8acd47e8ea505fa","target":"record","created_at":"2026-05-18T01:02:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"722d37bf1247d9d43eff91bfb40503b995081126f3c43d34540363a37033454a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-26T09:32:01Z","title_canon_sha256":"539f379781ae9c18e51a97c5ff980bbc52c26c26a604a94a7cfb80bea8cf3b8a"},"schema_version":"1.0","source":{"id":"1605.08206","kind":"arxiv","version":2}},"canonical_sha256":"6db3819c7dde73b1bce43f8ae2c9ffb663ee44e0bd7808ec994d6cfd505fa18f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6db3819c7dde73b1bce43f8ae2c9ffb663ee44e0bd7808ec994d6cfd505fa18f","first_computed_at":"2026-05-18T01:02:52.067658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:52.067658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uEzL09a2A7PkSynp97x7cl1vsWiFulw7s8VJSIyZ3LQeM/CWlY6NYWvAZzZdFvcyosChRucifQzexm/5J4ruAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:52.068114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08206","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa5ec28aa8ab92d4bc3f4c92d2457c93b3a6d1bad3f49b90c8acd47e8ea505fa","sha256:9654b4e345f5c33c83afc43b53c1bb5b63bfde146df13efef2fe10d18d8fd21d"],"state_sha256":"ed6f04298c07906966ca5d4fd717904b910a382f7e296c26555a8651bb713cd0"}