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For $1<p<\\infty$, consider the eigenvalue problem $$\n  \\left\\{ \\begin{array} [c]{ll} -\\Delta_{p}u=\\lambda m(x)|u|^{p-2}u & \\text{in }\\Omega,\\\\ u=0 & \\text{on }\\partial\\Omega, \\end{array} \\right. $$ where $\\Delta_{p}u$ is the usual $p$-Laplacian. Our purpose in this article is to study the limit as $p\\rightarrow\\infty$ for the eigenvalues $\\lambda _{k,p}\\left( m\\right) $ of the aforementioned problem. In addition, we describe the limit of some normalized associated ei"},"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":"1810.05696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-12T19:36:25Z","cross_cats_sorted":[],"title_canon_sha256":"516b950bb41a786f8bb2865e71afd181808b1de7d85839b80c8d7b5e83aecd3e","abstract_canon_sha256":"4c18021e6e816a130e456e489a7879b4f4c170c55f5af90393a4601e721cd370"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:27.211148Z","signature_b64":"zmJtFSlmG0dowpKHEsg8LyU4HIF7TLt8U1AhV2NSDh2JO5OGpCq25ghEF8w8X1jINPB4VkiGIr7AMbSqCQW4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09c6c01ca8ba05fe7e4da8845d2d8b9bdb6cd322cef47076a487c8170e97a910","last_reissued_at":"2026-05-18T00:03:27.210667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:27.210667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $\\infty$-eigenvalue problem with a sign-changing weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joana Terra, Julio D. Rossi, Uriel Kaufmann","submitted_at":"2018-10-12T19:36:25Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{n}$ be a smooth bounded domain and $m\\in C(\\overline{\\Omega})$ be a sign-changing weight function. For $1<p<\\infty$, consider the eigenvalue problem $$\n  \\left\\{ \\begin{array} [c]{ll} -\\Delta_{p}u=\\lambda m(x)|u|^{p-2}u & \\text{in }\\Omega,\\\\ u=0 & \\text{on }\\partial\\Omega, \\end{array} \\right. $$ where $\\Delta_{p}u$ is the usual $p$-Laplacian. Our purpose in this article is to study the limit as $p\\rightarrow\\infty$ for the eigenvalues $\\lambda _{k,p}\\left( m\\right) $ of the aforementioned problem. 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