{"paper":{"title":"Polyharmonic Kirchhoff type equations with singular exponential nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K. Sreenadh, Pawan Kumar Mishra, Sarika Goyal","submitted_at":"2016-04-01T07:20:09Z","abstract_excerpt":"\\noi In this article, we study the existence of non-negative solutions of the following polyharmonic Kirchhoff type problem with critical singular exponential nolinearity $$ \\quad \\left\\{ \\begin{array}{lr}\n  \\quad -M\\left(\\displaystyle\\int_\\Omega |\\nabla^m u|^{\\frac{n}{m}}dx\\right)\\Delta_{\\frac{n}{m}}^{m} u = \\frac{f(x,u)}{|x|^\\alpha} \\; \\text{in}\\; \\Om{,}\n  \\quad \\quad u = \\nabla u=\\cdot\\cdot\\cdot= {\\nabla}^{m-1} u=0 \\quad \\text{on} \\quad \\partial \\Om{,} \\end{array} \\right. $$ where $\\Om\\subset \\mb R^n$ is a bounded domain with smooth boundary, $n\\geq 2m\\geq 2$ and $f(x,u)$ behaves like $e^{|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00155","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":""},"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"}