{"paper":{"title":"Semilinear elliptic PDE's with biharmonic operator and a singular potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mousomi Bhakta","submitted_at":"2015-06-03T04:47:32Z","abstract_excerpt":"We study the existence/nonexistence of positive solution to the problem of the type: \\begin{equation}\\tag{$P_{\\lambda}$} \\begin{cases} \\Delta^2u-\\mu a(x)u=f(u)+\\lambda b(x)\\quad\\textrm{in $\\Omega$,}\\\\ u>0 \\quad\\textrm{in $\\Omega$,}\\\\ u=0=\\Delta u \\quad\\textrm{on $\\partial\\Omega$,} \\end{cases} \\end{equation} where $\\Omega$ is a smooth bounded domain in $\\mathbb R^N$, $N\\geq 5$, $a, b, f$ are nonnegaive functions satisfying certain hypothesis which we will specify later. $\\mu,\\lambda$ are positive constants. Under some suitable conditions on functions $a, b, f$ and the constant $\\mu$, we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01122","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}