{"paper":{"title":"Existence of positive solutions for a Brezis--Nirenberg type problem involving an inverse operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Ortega, Eduardo Colorado, Pablo \\'Alvarez-Caudevilla","submitted_at":"2019-03-11T15:01:16Z","abstract_excerpt":"This paper is devoted to the existence of positive solutions for a problem related to a fourth-order differential equation involving a nonlinear term depending on a second order differential operator, $$(-\\Delta)^2 u=\\lambda u+ (-\\Delta)|u|^{p-1}u,$$ in a bounded domain $\\Omega\\subset\\mathbb{R}^N$, $N\\geq 7$, and assuming homogeneous Navier boundary conditions. In particular, we study a second order equation involving a nonlocal term of the form, $$-\\Delta u=\\lambda (-\\Delta)^{-1} u+|u|^{p-1}u,$$ under Dirichlet boundary conditions and we prove the existence of positive solutions depending on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04345","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"}