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Duran","submitted_at":"2010-11-01T19:05:59Z","abstract_excerpt":"This work deals with the system $(-\\Delta)^m u= a(x) v^p$, $(-\\Delta)^m v=b(x) u^q$ with Dirichlet boundary condition in a domain $\\Omega\\subset\\RR^n$, where $\\Omega$ is a ball if $n\\ge 3$ or a smooth perturbation of a ball when $n=2$.\n  We prove that, under appropriate conditions on the parameters ($a,b,p,q,m,n$), any non-negative solution $(u,v)$ of the system is bounded by a constant independent of $(u,v)$. Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary.\n  The case $m=1$ was considered by Souplet "},"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":"1011.0412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-01T19:05:59Z","cross_cats_sorted":[],"title_canon_sha256":"24d3a3198a8b27956e5622c71c95a9dda42244e8e1972557a79f5cd26e901498","abstract_canon_sha256":"6c1ff59b1d2a985829793e18903c99ef044fe122a6214e712824018d67d813f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:09.215526Z","signature_b64":"9WWgy+9WGQc2pEJfrPsp1bo2VtsvxBkm5bz1WL8tbSDNuDNN0P5O3En+hXeY9HY4w+p3EEizJeMexeVSbkQLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21ca85ae9c31e08a4e400491b99698446c05582a053ce8f280e306fda5920138","last_reissued_at":"2026-05-18T04:36:09.214873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:09.214873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of bounded solutions for a nonlinear elliptic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marcela Sanmartino, Marisa Toschi, Ricardo G. 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