{"paper":{"title":"On some weakly coercive quasilinear problems with forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrzej Szulkin, Michel Willem","submitted_at":"2017-09-15T13:19:30Z","abstract_excerpt":"We consider the forced problem $-\\Delta_p u - V(x)|u|^{p-2} u = f(x)$, where $\\Delta_p$ is the $p$-Laplacian ($1<p<\\infty$) in a domain $\\Omega\\subset \\mathbb{R}^N$, $V\\ge 0$ and $Q_V (u) := \\int_\\Omega |\\nabla u|^p\\, dx - \\int_\\Omega V|u|^p\\,dx$ satisfies the condition (A) stated at the beginning of the paper. We show that this problem has a solution for all $f$ in a suitable space of distributions. Then we apply this result to some classes of functions $V$ which in particular include the Hardy potential and the potential $V(x)=\\lambda_{1,p}(\\Omega)$, where $\\lambda_{1,p}(\\Omega)$ is the Poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05187","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"}