{"paper":{"title":"Qualitative properties of positive solutions of a mixed order nonlinear Schr\\\"{o}dinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Jiwen Zhang, Serena Dipierro, Xifeng SU","submitted_at":"2024-11-15T04:38:14Z","abstract_excerpt":"In this paper, we deal with the following mixed local/nonlocal Schr\\\"{o}dinger equation\n  \\begin{equation*}\n  \\left\\{\n  \\begin{array}{ll}\n  - \\Delta u + (-\\Delta)^s u+u = u^p \\quad \\hbox{in $\\mathbb{R}^n$,}\n  u>0 \\quad \\hbox{in $\\mathbb{R}^n$,}\n  \\lim\\limits_{|x|\\to+\\infty}u(x)=0,\n  \\end{array}\n  \\right.\n  \\end{equation*} where $n\\geqslant2$, $s\\in (0,1)$ and $p\\in\\left(1,\\frac{n+2}{n-2}\\right)$.\n  The existence of positive solutions for the above problem is proved, relying on some new regularity results. In addition, we study the power-type decay and the radial symmetry properties of such sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09941","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.09941/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}