{"paper":{"title":"Nonlocal Pertubations of Fractional Choquard Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gurpreet Singh","submitted_at":"2017-05-16T15:49:48Z","abstract_excerpt":"We study the equation \\begin{equation} (-\\Delta)^{s}u+V(x)u= (I_{\\alpha}*|u|^{p})|u|^{p-2}u+\\lambda(I_{\\beta}*|u|^{q})|u|^{q-2}u \\quad\\mbox{ in } \\R^{N}, \\end{equation} where $I_\\gamma(x)=|x|^{-\\gamma}$ for any $\\gamma\\in (0,N)$, $p, q >0$, $\\alpha,\\beta\\in (0,N)$, $N\\geq 3$ and $ \\lambda \\in R$. First, the existence of a groundstate solutions using minimization method on the associated Nehari manifold is obtained. Next, the existence of least energy sign-changing solutions is investigated by considering the Nehari nodal set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05775","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"}