{"paper":{"title":"Infinitely many sign-changing solutions for Kirchhoff type problems in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bo\\v{s}tjan Gabrov\\v{s}ek, Jijiang Sun, Lin Li, Matija Cencelj","submitted_at":"2019-07-03T12:34:24Z","abstract_excerpt":"In this paper, we consider the following nonlinear Kirchhoff type problem: \\[ \\left\\{\\begin{array}{lcl}-\\left(a+b\\displaystyle\\int_{\\mathbb{R}^3}|\\nabla u|^2\\right)\\Delta u+V(x)u=f(u), & \\textrm{in}\\,\\,\\mathbb{R}^3,\\\\ u\\in H^1(\\mathbb{R}^3), \\end{array}\\right. \\] where $a,b>0$ are constants, the nonlinearity $f$ is superlinear at infinity with subcritical growth and $V$ is continuous and coercive. For the case when $f$ is odd in $u$ we obtain infinitely many sign-changing solutions for the above problem by using a combination of invariant sets method and the Ljusternik-Schnirelman type minimax"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01888","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"}