{"paper":{"title":"Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Divya Goel, K. Sreenadh","submitted_at":"2019-01-31T11:28:10Z","abstract_excerpt":"We consider the following Kirchhoff - Choquard equation \\[ -M(\\|\\na u\\|_{L^2}^{2})\\De u = \\la f(x)|u|^{q-2}u+ \\left(\\int_{\\Om}\\frac{|u(y)|^{2^*_{\\mu}}}{|x-y|^{\\mu}}dy\\right)|u|^{2^*_{\\mu}-2}u \\; \\text{in}\\; \\Om,\\quad\n  u = 0 \\; \\text{ on } \\pa \\Om , \\]\n  where $\\Om$ is a bounded domain in $\\mathbb{R}^N( N\\geq 3)$ with $C^2$ boundary, $2^*_{\\mu}=\\frac{2N-\\mu}{N-2}$, $1<q\\leq 2$, and $f$ is a continuous real valued sign changing function. When $1<q< 2$, using the method of Nehari manifold and Concentration-compactness Lemma, we prove the existence and multiplicity of positive solutions of the ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11310","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"}