{"paper":{"title":"The Nehari manifold for indefinite Kirchhoff problem with Caffarelli-Kohn-Nirenberg type critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David G. Costa, Joao Marcos do \\'O, Pawan Kumar Mishra","submitted_at":"2019-06-25T19:14:56Z","abstract_excerpt":"In this paper we study the following class of nonlocal {problems} involving Caffarelli-Kohn-Nirenberg type critical growth\n  \\begin{align*}\n  L(u)&-\\lambda h(x)|x|^{-2(1+a)}u=\\mu f(x)|u|^{q-2}u+|x|^{-pb}|u|^{p-2}u\\;\\; \\text{in } \\mathbb R^N,\n  \\end{align*}\n  where\n  $h(x)\\geq 0$, $f(x)$ is a continuous function which may change sign, $\\lambda, \\mu$ are positive real parameters and $1<q<2$, $4< p=2N/[N+2(b-a)-2]$, $0\\leq a<b<a+1<N/2$, $N\\geq 3$. Here\n  $$\n  L(u)=-M\\left(\\int_{\\mathbb R^N} |x|^{-2a}|\\nabla u|^2dx\\right)\\mathrm {div}(|x|^{-2a}\\nabla u)\n  $$\n  and the function $M:\\mathbb R^+\\cup \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10730","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"}