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Repov\\v{s}, Giovanni Molica Bisci, Vincenzo Ambrosio","submitted_at":"2016-11-06T12:03:00Z","abstract_excerpt":"In this paper we discuss the existence and non-existence of weak solutions to parametric fractional equations involving the square root of the Laplacian $A_{1/2}$ in a smooth bounded domain $\\Omega\\subset \\mathbb{R}^n$ ($n\\geq 2$) and with zero Dirichlet boundary conditions. Namely, our simple model is the following equation \\begin{equation*} \\left\\{ \\begin{array}{ll} A_{1/2}u=\\lambda f(u) & \\mbox{ in } \\Omega\\\\ u=0 & \\mbox{ on } \\partial\\Omega. \\end{array}\\right. \\end{equation*} The existence of at least two non-trivial $L^{\\infty}$-bounded weak solutions is established for large value of the"},"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":"1611.01763","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-06T12:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"f6dbbc8a1c92476d74b15ab94dad31923340d2684eaa33739a36271a6e275430","abstract_canon_sha256":"5229d20b355250ccb68f5e36396c785d3034e6c1583d3f2ce885f08b9ae91508"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:37.349266Z","signature_b64":"THxHSwCj2xVYP5SLrqRaWuLLXqJmc3iPrmT+3F44xSuuD9IcL3H8kY+5xGrMtJdt3QTxp3OKXdk5BnPTBnZ+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b783e45cd39f2d513f29efe4c3e920fe83aaf9c912bc5cc91033473bde0ece74","last_reissued_at":"2026-05-17T23:39:37.348636Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:37.348636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear equations involving the square root of the Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Du\\v{s}an D. 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