{"paper":{"title":"Multi-bubble nodal solutions to slightly subcritical elliptic problems with Hardy terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qianqiao Guo, Thomas Bartsch","submitted_at":"2015-08-17T12:58:01Z","abstract_excerpt":"The paper is concerned with the slightly subcritical elliptic problem with Hardy term \\[ \\left\\{ \\begin{aligned} -\\Delta u-\\mu\\frac{u}{|x|^2} &= |u|^{2^{\\ast}-2-\\epsilon}u &&\\quad \\text{in } \\Omega, \\\\\\ u &= 0&&\\quad \\text{on } \\partial\\Omega, \\end{aligned} \\right. \\] in a bounded domain $\\Omega\\subset\\mathbb{R}^N$ with $0\\in\\Omega$, in dimensions $N\\ge7$. We prove the existence of multi-bubble nodal solutions that blow up positively at the origin and negatively at a different point as $\\epsilon\\to0$ and $\\mu=\\epsilon^\\alpha$ with $\\alpha>\\frac{N-4}{N-2}$. In the case of $\\Omega$ being a ball "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04007","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"}