{"paper":{"title":"On finding solutions of a Kirchhoff type problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yisheng Huang, Yuanze Wu, Zeng Liu","submitted_at":"2015-07-20T06:30:29Z","abstract_excerpt":"Consider the following Kirchhoff type problem $$ \\left\\{\\aligned -\\bigg(a+b\\int_{\\mathbb{B}_R}|\\nabla u|^2dx\\bigg)\\Delta u&= \\lambda u^{q-1} + \\mu u^{p-1}, &\\quad \\text{in}\\mathbb{B}_R, \\\\ u&>0,&\\quad\\text{in}\\mathbb{B}_R,\\\\ u&=0,&\\quad\\text{on}\\partial\\mathbb{B}_R, \\endaligned \\right.\\eqno{(\\mathcal{P})} $$ where $\\mathbb{B}_R\\subset \\bbr^N(N\\geq3)$ is a ball, $2\\leq q<p\\leq2^*:=\\frac{2N}{N-2}$ and $a$, $b$, $\\lambda$, $\\mu$ are positive parameters. By introducing some new ideas and using the well-known results of the problem $(\\mathcal{P})$ in the cases of $a=\\mu=1$ and $b=0$, we obtain some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05392","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"}