{"paper":{"title":"A perturbation approach to studying sign-changing solutions of Kirchhoff equations with a general nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianjun Zhang, Yijun Lou, Zhisu Liu","submitted_at":"2018-12-19T14:28:52Z","abstract_excerpt":"By employing a novel perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutions to a class of semilinear Kirchhoff equations in the following form $$ -\\left(a+ b\\int_{\\R^3}|\\nabla u|^2\\right)\\triangle {u}+V(x)u=f(u),\\,\\,x\\in\\R^3, $$ where $a,b>0$ are constants, $V\\in C(\\R^3,\\R)$, $f\\in C(\\R,\\R)$. The methodology proposed in the current paper is robust, in the sense that, the monotonicity condition for the nonlinearity $f$ and the coercivity condition of $V$ are not required. Our result improv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09240","kind":"arxiv","version":2},"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"}