{"paper":{"title":"Polyharmonic $k-$Hessian equations in $\\mathbb{R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.SP"],"primary_cat":"math.AP","authors_text":"Carlos Escudero, Pedro Balodis","submitted_at":"2016-03-30T21:39:32Z","abstract_excerpt":"This work is focused on the study of the nonlinear elliptic higher order equation \\begin{equation}\\nonumber \\left( -\\Delta \\right)^m u = S_k[-u] + \\lambda f, \\qquad x \\in \\mathbb{R}^N, \\end{equation} where the $k-$Hessian $S_k[u]$ is the $k^{\\mathrm{th}}$ elementary symmetric polynomial of eigenvalues of the Hessian matrix of the solution and the datum $f$ belongs to a suitable functional space. This problem is posed in $\\mathbb{R}^N$ and we prove the existence of at least one solution by means of topological fixed point methods for suitable values of $m \\in \\mathbb{N}$. Questions related to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09392","kind":"arxiv","version":3},"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"}