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We require that $K\\left( x\\right)$ and $a\\left( x\\right) $ are nonnegative functions in $\\mathbb{R}^{3}$ and satisfy some suitable assumptions, but not requiring any symmetry property on them. Assuming that $\\lim_{\\left\\vert x\\right\\vert \\rightarrow \\infty }K"},"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":"1408.4302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-19T11:41:14Z","cross_cats_sorted":[],"title_canon_sha256":"4ab68c1d473f9f1d59a6108eb1e86bddde7c9411942779b2282ae1c9548c2a2d","abstract_canon_sha256":"2fc7cee172ea14e504c48f7d945d54258cb6b0106430a390d220d92134186aa9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:56.991699Z","signature_b64":"sYhC98a3VPHRyWDpgQ/dPY5CX/dg+7smLCPITFzYd7uafSB3u8oEWuyY6dUTX/Y7ibJpQmiJDEzad1cPHC22Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5eea2a68d3039ef5bd5f9ef561ce498239b5c8c36114cd2f119d6a3388ac940","last_reissued_at":"2026-05-18T02:27:56.991212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:56.991212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the non-autonomous Schr\\\"odinger-Poisson problems in $\\mathbb{R}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu","submitted_at":"2014-08-19T11:41:14Z","abstract_excerpt":"In this paper, we study the problem: \\begin{equation*} \\left\\{ \\begin{array}{ll} -\\Delta u+u+\\lambda K\\left( x\\right) \\phi u=a\\left( x\\right) \\left\\vert u\\right\\vert ^{p-2}u & \\text{ in }\\mathbb{R}^{3}, \\\\ -\\Delta \\phi =K\\left( x\\right) u^{2} & \\ \\text{in }\\mathbb{R}^{3}, \\end{array} \\right. \\end{equation*} where $\\lambda >0$ and $2<p<4$. We require that $K\\left( x\\right)$ and $a\\left( x\\right) $ are nonnegative functions in $\\mathbb{R}^{3}$ and satisfy some suitable assumptions, but not requiring any symmetry property on them. 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