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In the purely $L^p$-subcritical case, we obtain the existence of ground state solution by virtue of truncation technique, and obtain multiplicity of normalized solutions. In the purely $L^p$-critical and supercritical case, we drive the existence of positive ground state solution"},"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":"2306.10207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-16T23:05:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2114f6f932bee9d5954e581a17ceee4d981c20aace9f454c830427039fcac9cf","abstract_canon_sha256":"4846509ab364101891d5854cb3b3389319a8df54565eaec99e7491cce11d63e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:21:35.308833Z","signature_b64":"24x07KMe7z7NJrSi3XTmQHPgbnTbrqnIBRQqkn9O5z8J0JLGb9SI+53FNxTOn6pB20568MnXZz2vKrjFu10hAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56ef91ce5ea0d6595dc9364e125749213e7951aebfd46ba2a902cdc545f49360","last_reissued_at":"2026-07-05T06:21:35.308362Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:21:35.308362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normalized solutions for some quasilinear elliptic equation with critical Sobolev exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Xiaojing Feng, Yuhua Li","submitted_at":"2023-06-16T23:05:52Z","abstract_excerpt":"Consider the equation \\begin{equation*} -\\Delta_p u =\\lambda |u|^{p-2}u+\\mu|u|^{q-2}u+|u|^{p^\\ast-2}u\\ \\ {\\rm in}\\ \\R^N \\end{equation*} under the normalized constraint $$\\int_{ \\R^N}|u|^p=c^p,$$ where $-\\Delta_pu={\\rm div} (|\\nabla u|^{p-2}\\nabla u)$, $1<p<N$, $p<q<p^\\ast=\\frac{Np}{N-p}$, $c,\\mu>0$ and $\\lambda\\in\\R$. In the purely $L^p$-subcritical case, we obtain the existence of ground state solution by virtue of truncation technique, and obtain multiplicity of normalized solutions. 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