{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:02:00Z","timestamp":1760144520795,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,4,27]],"date-time":"2024-04-27T00:00:00Z","timestamp":1714176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2020A1515110706","GC300501-100","202301AT070465"],"award-info":[{"award-number":["2020A1515110706","GC300501-100","202301AT070465"]}]},{"name":"Research Startup Funds of DGUT","award":["2020A1515110706","GC300501-100","202301AT070465"],"award-info":[{"award-number":["2020A1515110706","GC300501-100","202301AT070465"]}]},{"name":"Yunnan Fundamental Research Projects","award":["2020A1515110706","GC300501-100","202301AT070465"],"award-info":[{"award-number":["2020A1515110706","GC300501-100","202301AT070465"]}]},{"name":"Xingdian Talent Support Program for Young Talents of Yunnan Province","award":["2020A1515110706","GC300501-100","202301AT070465"],"award-info":[{"award-number":["2020A1515110706","GC300501-100","202301AT070465"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the following non-local problem in fractional Orlicz\u2013Sobolev spaces: (\u2212\u0394\u03a6)su+V(x)a(|u|)u=f(x,u),\u00a0x\u2208RN, where (\u2212\u0394\u03a6)s(s\u2208(0,1)) denotes the non-local and maybe non-homogeneous operator, the so-called fractional \u03a6-Laplacian. Without assuming the Ambrosetti\u2013Rabinowitz type and the Nehari type conditions on the non-linearity f, we obtain the existence of ground state solutions for the above problem with periodic potential function V(x). The proof is based on a variant version of the mountain pass theorem and a Lions\u2019 type result in fractional Orlicz\u2013Sobolev spaces.<\/jats:p>","DOI":"10.3390\/axioms13050294","type":"journal-article","created":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T10:33:36Z","timestamp":1714386816000},"page":"294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ground State Solutions for a Non-Local Type Problem in Fractional Orlicz Sobolev Spaces"],"prefix":"10.3390","volume":"13","author":[{"given":"Liben","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China"}]},{"given":"Xingyong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"}]},{"given":"Cuiling","family":"Liu","sequence":"additional","affiliation":[{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/S0375-9601(00)00201-2","article-title":"Fractional quantum mechanics and L\u00e9vy path integrals","volume":"268","author":"Laskin","year":"2000","journal-title":"Phys. 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