{"paper":{"title":"Solutions of super-linear elliptic equations and their Morse indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Foued Mtiri","submitted_at":"2020-07-20T07:45:17Z","abstract_excerpt":"We investigate here the degenerate bi-harmonic equation: $$\\Delta_{m}^2 u=f(x,u)\\; \\;\\;\\mbox{in} \\O,\\quad u = \\Delta u = 0\\quad \\mbox{on }\\; \\p\\Omega,$$ with $m\\ge 2,$ and also the degenerate tri-harmonic equation: $$ -\\Delta_{m}^3 u=f(x,u)\\;\\;\\; \\mbox{in} \\O,\\quad u = \\frac{\\p u}{\\p \\nu} = \\frac{\\p^{2} u}{\\p\\nu^{2}} = 0\\quad \\mbox{on }\\; \\p\\Omega,$$ where $\\Omega\\subset \\mathbb{R}^{N}$ is a bounded domain with smooth boundary $N>4$ or $N>6$ resp, and $f \\in \\mathrm{C}^{1}(\\Omega\\times \\mathbb{R})$ satisfying suitable m-superlinear and subcritical growth conditions. Our main purpose is to esta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.10838","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.10838/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}