{"paper":{"title":"Multiple Semiclassical Standing Waves for Fractional Nonlinear Schr\\\"{o}dinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guoyuan Chen","submitted_at":"2014-05-17T08:18:44Z","abstract_excerpt":"Via a Lyapunov-Schmidt reduction, we obtain multiple semiclassical solutions to a class of fractional nonlinear Schr\\\"odinger equations. Precisely, we consider \\begin{equation*} \\varepsilon^{2s}(-\\Delta)^{s}u+u+V(x)u=|u|^{p-1}u,\\quad u\\in H^s(\\mathbf R^n), \\end{equation*} where $0<s<1$, $n>4-4s$, $1<p<\\frac{n+2s}{n-2s}$ (if $n>2s$) and $1<p<\\infty$ (if $n\\le 2s$), $V(x)$ is a non-negative potential function. If $V$ is a sufficiently smooth bounded function with a non-degenerate compact critical manifold $M$, then, when $\\varepsilon$ is sufficiently small, there exist at least $l(M)$ semiclassi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4366","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"}