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We also consider the special case\n  \\[\\boldsymbol{f}(x,\\boldsymbol{u})=\\lambda|\\boldsymbol{u}|^{p-2}\\boldsymbol{u}+|\\boldsymbol{u}|^{q-2}\\boldsymbol{u},\\] and we prove a classification result. In particular, we show that any least ener"},"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":"2510.15694","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-10-17T14:37:10Z","cross_cats_sorted":[],"title_canon_sha256":"f63e2b888860220339f7f5620c122c77f7a1764f613026679ece39ae9b73db47","abstract_canon_sha256":"3356ee14131c8256f41e50fdbc95fd918bd8d779643b968885926fbcd40ee79d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T02:23:19.349512Z","signature_b64":"afI2FPGJPdO736WyL62/khCsd2i0i6jZpCMLtV12Gxbzorsng3kxsVQLg3bZMqR1eGRDgDOLTEnpiHBa2FBNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a343eea1b614813e5306d582cfe4275ba0eb6e4e46d5465cfe8eb0c051b7b06","last_reissued_at":"2026-07-28T02:23:19.348511Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T02:23:19.348511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence results for variational quasilinear elliptic systems involving the vectorial $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Annamaria Canino, Simone Mauro","submitted_at":"2025-10-17T14:37:10Z","abstract_excerpt":"We prove existence and regularity results for the following elliptic system: \\[ \\begin{cases} -\\textbf{div}(|D\\boldsymbol{u}|^{p-2}D\\boldsymbol{u})=\\boldsymbol{f}(x,\\boldsymbol{u}) & \\text{in } \\Omega \\\\ \\boldsymbol{u}=0 & \\text{on } \\partial\\Omega, \\end{cases} \\] where $\\boldsymbol{u}=(u^1,\\dots,u^m)$, $p>1$, and $\\Omega\\subset\\mathbb{R}^N$ is a bounded domain. We also consider the special case\n  \\[\\boldsymbol{f}(x,\\boldsymbol{u})=\\lambda|\\boldsymbol{u}|^{p-2}\\boldsymbol{u}+|\\boldsymbol{u}|^{q-2}\\boldsymbol{u},\\] and we prove a classification result. 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