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Figueiredo","submitted_at":"2017-07-17T18:30:31Z","abstract_excerpt":"In this paper we consider the following quasilinear Schr\\\"odinger-Poisson system $$ \\left\\{ \\begin{array}[c]{ll} - \\Delta u +u+\\phi u = \\lambda f(x,u)+|u|^{2^{*}-2}u &\\ \\mbox{in } \\mathbb{R}^{3} \\\\ -\\Delta \\phi -\\varepsilon^{4} \\Delta_4 \\phi = u^{2} & \\ \\mbox{in } \\mathbb{R}^{3}, \\end{array}\n  \\right. $$ depending on the two parameters $\\lambda,\\varepsilon>0$.\n  We first prove that, for $\\lambda$ larger then a certain $\\lambda^{*}>0$, there exists a solution for every $\\varepsilon>0$. Later, we study the asymptotic behaviour of these solutions whenever $\\varepsilon$ tends to zero, and we prove"},"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":"1707.05353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T18:30:31Z","cross_cats_sorted":[],"title_canon_sha256":"dade9d3191e01774839c18f6a7f1769de54364035238bb4f1f3eb45070a89c6d","abstract_canon_sha256":"6f80c7eeb4651cb846f50b93427ebe5203bb4621195c08129f03eecc0d996883"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:02.572115Z","signature_b64":"FNvX2uvvaRtjtmNxAwJMo38iFQRBT9UxUThn3flGQa1ZFXXzH7DG7uHJfK3dVuhk+H7iUR05fq1sCWDKbWcQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdfc96ae2adabcac125d7e61032d8f69070d6c8ffe979f7ca6a85958c30b4f89","last_reissued_at":"2026-05-18T00:40:02.571620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:02.571620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and asymptotic behaviour of solutions for a quasi-linear schrodinger-poisson system under a critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Giovany M. Figueiredo","submitted_at":"2017-07-17T18:30:31Z","abstract_excerpt":"In this paper we consider the following quasilinear Schr\\\"odinger-Poisson system $$ \\left\\{ \\begin{array}[c]{ll} - \\Delta u +u+\\phi u = \\lambda f(x,u)+|u|^{2^{*}-2}u &\\ \\mbox{in } \\mathbb{R}^{3} \\\\ -\\Delta \\phi -\\varepsilon^{4} \\Delta_4 \\phi = u^{2} & \\ \\mbox{in } \\mathbb{R}^{3}, \\end{array}\n  \\right. $$ depending on the two parameters $\\lambda,\\varepsilon>0$.\n  We first prove that, for $\\lambda$ larger then a certain $\\lambda^{*}>0$, there exists a solution for every $\\varepsilon>0$. 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