{"paper":{"title":"Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hichem Ounaies, Sabri Bahrouni","submitted_at":"2019-09-14T11:55:12Z","abstract_excerpt":"In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional Orlicz-Sobolev Schr\\\"{o}dinger equations whose simplest prototype is $$(-\\triangle)^{s}_{m}u+V(x)m(u)=f(x,u),\\ x\\in\\mathbb{R}^{d},$$ where $0<s<1$, $d\\geq2$ and $(-\\triangle)^{s}_{m}$ is the fractional $M$-Laplace operator. The proof is based on the variant Fountain theorem established by Zou."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.06584","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/1909.06584/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"}