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By applying the method of penalized functions, the existence of one nontrivial solution for such system in the less-studied case $3<p\\leq4$ is obtained for $"},"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":"1412.5463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-17T16:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"ea8e67fdd12cba734b76e3feebade1c3b5bfc359f7e9415a907c33192d580a37","abstract_canon_sha256":"8fffeef7b038b2db57d426714579be0c68a676d7f0aa2e458d975c2d9f5ad4d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:02.914495Z","signature_b64":"bTHnBvrkvgeRcH2b4vBrbZFl9oh4VlHP+Zv+G6pHp3WrxsGQpq9p59xOegnHsH5kwoxGHsvU/MYFPcxD8MgIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53ae21932c456963c863fe5e5f9a0a93eb3a79b71400bffac16228bfff8440f4","last_reissued_at":"2026-05-18T02:31:02.914104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:02.914104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Schr\\\"odinger-Poisson system with steep potential well and indefinite potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu, Yuanze Wu","submitted_at":"2014-12-17T16:23:46Z","abstract_excerpt":"In this paper, we study the following Schr\\\"odinger-Poisson system: $$ \\left\\{\\aligned&-\\Delta u+V_\\lambda(x)u+K(x)\\phi u=f(x,u)&\\quad\\text{in }\\bbr^3,\\\\ &-\\Delta\\phi=K(x)u^2&\\quad\\text{in }\\bbr^3,\\\\ &(u,\\phi)\\in\\h\\times\\D,\\endaligned\\right.\\eqno{(\\mathcal{SP}_{\\lambda})} $$ where $V_\\lambda(x)=\\lambda a(x)+b(x)$ with a positive parameter $\\lambda$, $K(x)\\geq0$ and $f(x,t)$ is continuous including the power-type nonlinearity $|u|^{p-2}u$. 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