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The first problem is the mixed nonlinear-Neumann boundary value problem $$ \\left\\{\n  \\begin{array}{ll}\n  \\displaystyle -\\Delta u=f(u) &{\\rm in}\\quad \\R, \\\\ \\displaystyle \\\\ \\frac{\\partial u}{\\partial \\nu}=g(u) &{\\rm on}\\quad \\Gamma_1,\\\\ \\displaystyle \\\\ \\frac{\\partial u}{\\partial \\nu}=0 &{\\rm on}\\quad \\Gamma_0 \\end{array} \\right. $$ and the second is the nonlinear-Dirichlet boundary value problem $$ \\left\\{\n  \\begin{array}{ll}\n  \\displaystyle -\\Delta u=f(u) &{\\rm in}\\quad \\R, \\\\ "},"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":"1410.5157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-20T05:56:41Z","cross_cats_sorted":[],"title_canon_sha256":"f65626d29cc4bd8d7b786aebbfa6bc132831cb23f143333dbcd914c521010670","abstract_canon_sha256":"ca7658bdb5cc28e3cd497d35815533f719522d1d8c96c9fe77e4fc62fdd7fd04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:46.717520Z","signature_b64":"uqfTxwgEjDYlDldxViym7h8jN0IGLZHYtYzUXQbr92KM44eR/zVYSTyZ6ONeNCBeq/52Bk8wPWv+TGBl73akCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86ff690ec603838812370f544270690c68d6a5e07f65d8b58c78634b74b7b93c","last_reissued_at":"2026-05-18T02:39:46.717124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:46.717124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville Type Theorems for Two Mixed Boundary Value Problems with General Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xiaohui Yu","submitted_at":"2014-10-20T05:56:41Z","abstract_excerpt":"In this paper, we study the nonexistence of positive solutions for the following two mixed boundary value problems. 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