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Under some proper assumptions on the nonnegative functions $K(x)$ and $f(x)$, but not requiring any symmetry property, when $\\lambda$ is sufficiently small, we find a bounded nodal solution for the above problem by proposing"},"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":"1812.03042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-07T14:39:47Z","cross_cats_sorted":[],"title_canon_sha256":"f9f7deb252b3ca9e006394cf18c7cdc63ce71f85ca0506f460a74aee52d9d552","abstract_canon_sha256":"16095ec9afd47dcb3f5b0b6882457a4b6f79e509f74867aced289410ec05898b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:51.102389Z","signature_b64":"Lubnsnk9ydEdyBL+PpjavJz8pWitNPGj8OxQv8aQIfhG6xbFBbONMDqKmBpX/rU1Y55LM6Ai1iQ6+ARl6GM+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"422b613d9262f351eb0e9fe27417d3e7ff068e65ecdbafd45af49380b5bd604e","last_reissued_at":"2026-05-17T23:58:51.101519Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:51.101519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bound state nodal solutions for the non-autonomous Schr\\\"{o}dinger--Poisson system 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":"2018-12-07T14:39:47Z","abstract_excerpt":"In this paper, we study the existence of nodal solutions for the non-autonomous Schr\\\"{o}dinger--Poisson system: \\begin{equation*} \\left\\{ \\begin{array}{ll} -\\Delta u+u+\\lambda K(x) \\phi u=f(x) |u|^{p-2}u & \\text{ in }\\mathbb{R}^{3}, \\\\ -\\Delta \\phi =K(x)u^{2} & \\text{ in }\\mathbb{R}^{3},% \\end{array}% \\right. \\end{equation*}% where $\\lambda >0$ is a parameter and $2<p<4$. 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