{"paper":{"title":"Multi-bump solutions for Choquard equation with deepening potential well","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Al\\^annio B. N\\'obrega, Claudianor O. Alves, Minbo Yang","submitted_at":"2015-10-06T01:33:08Z","abstract_excerpt":"We study the existence of multi-bump solutions to Choquard equation $$ \\begin{array}{ll} -\\Delta u + (\\lambda a(x)+1)u=\\displaystyle\\big(\\frac{1}{|x|^{\\mu}}\\ast |u|^p\\big)|u|^{p-2}u \\mbox{ in } \\,\\,\\, \\R^3, \\end{array} $$ where $\\mu \\in (0,3), p\\in(2, 6-\\mu)$, $\\lambda$ is a positive parameter and the nonnegative function $a(x)$ has a potential well $ \\Omega:=int (a^{-1}(0))$ consisting of $k$ disjoint bounded components $ \\Omega:=\\cup_{j=1}^{k}\\Omega_j$. We prove that if the parameter $\\lambda$ is large enough then the equation has at least $2^{k}-1$ multi-bump solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01409","kind":"arxiv","version":3},"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"}