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Consider the following singularly perturbed elliptic problem on $A$\n  \\begin{equation}\n  \\begin{array}{lll}\n  -\\eps^2{\\De u} + |x|^{\\alpha}u = |x|^{\\alpha}u^p, &\\mbox{\\qquad in} A \\notag u>0 &\\mbox{\\qquad in} A\n  \\frac{\\partial u}{\\partial\\nu} = 0 &\\mbox{\\qquad on} \\partial A\n  \\end{array} %\\label{a1}\n  \\end{equation} $1<p<2^*-1$. We shall show that there exists a positive solution $u_\\eps$ concentrating on an $S^1$ orbit as $\\eps\\to 0$. We prove this by reducing the problem to a lower dimensional one and analyzing a single point concent","authors_text":"B.B.Manna, P.N.Srikanth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-22T08:21:42Z","title":"On the solutions of a singular elliptic equation concentrating on a circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5831","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a1d2ae657b099aa8ed288ad21596c9c9f8d7b8eb63eb35b81a829c29b1919f00","target":"record","created_at":"2026-05-18T03:09:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4e673c0f0969db14386434a18ddb5f75ad64d63c7acfff89ea87e2a4c15f9044","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-22T08:21:42Z","title_canon_sha256":"34e121df14c4b3157b96b47c6d1b309a15954dda6747861a7187eaafaa1d90bc"},"schema_version":"1.0","source":{"id":"1310.5831","kind":"arxiv","version":1}},"canonical_sha256":"6bec12690d2ccf5160d841cc53ecbfe43ca5eed9cc312dbac13da833463d23eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bec12690d2ccf5160d841cc53ecbfe43ca5eed9cc312dbac13da833463d23eb","first_computed_at":"2026-05-18T03:09:32.096485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:32.096485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pop4m69o15sy6Cz6DlZ9zDMn9Gqg9gSZBI1MDWnnFh+kc/+0YT8WacQh1PueIjG5DSnZVZpX743ugFCiB7UlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:32.097135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1d2ae657b099aa8ed288ad21596c9c9f8d7b8eb63eb35b81a829c29b1919f00","sha256:91366a0ef516f5388bc9da9f8778c7ff5a34c167e505b0619fba12d2735f32db"],"state_sha256":"4a94ddda2c837c46f37796123c34a2463ebfc47cb5dd09dba08ece4f91e495f6"}