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Under this new set of assumptions, we manage to verify the Cerami compactness condition. Therefore, we succeed in proving the existen"},"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":"1607.00581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-03T02:41:08Z","cross_cats_sorted":[],"title_canon_sha256":"6c9082466278be813915d17f83186bfc5ed58a28068602ab0d4963c90f5ee919","abstract_canon_sha256":"8a0287c012f004a9b578d8e55cfaf9b25036bb53988ad0ed807713f6133739b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:34.695253Z","signature_b64":"CQPZFAk/rC2RLhKKz52v8AO3RrRU7ebTmlgiV/6hoRVfYIZI8a5UHcNAkPTzfpC9nLsS1BTry87qPSa0vcZzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98c58a8afdab0a9e3060296a36f8309f923d4b3e9ae19ad83dea21316d2260b6","last_reissued_at":"2026-05-18T01:11:34.694810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:34.694810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity of strong solutions for a class of elliptic problems without the Ambrosetti-Rabinowitz condition in $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunshan Zhao, Jinghua Yao, Li Yin, Qihu Zhang","submitted_at":"2016-07-03T02:41:08Z","abstract_excerpt":"We investigate the existence and multiplicity of solutions to the following $p(x)$-Laplacian problem in $\\mathbb{R}^{N}$ via critical point theory \\begin{equation*} \\left\\{ \\begin{array}{l} -\\bigtriangleup _{p(x)}u+V(x)\\left\\vert u\\right\\vert ^{p(x)-2}u=f(x,u),\\text{ in } \\mathbb{R}^{N}, \\\\ u\\in W^{1,p(\\cdot )}(\\mathbb{R}^{N}). \\end{array} \\right. \\end{equation*} We propose a new set of growth conditions which matches the variable exponent nature of the problem. 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