{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:31:06Z","timestamp":1760232666730,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,23]],"date-time":"2022-11-23T00:00:00Z","timestamp":1669161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider the following class of the fractional p&amp;q-Laplacian problem: (\u2212\u0394)psu+(\u2212\u0394)qsu+V(x)(|u|p\u22122u+|u|q\u22122u)+g(x)|u|r\u22122u=K(x)f(x,u)+h(u),x\u2208RN,V:RN\u2192R+ is a potential function, and h:R\u2192R is a perturbation term. We studied two cases: if f(x,u) is sublinear, by means of Clark\u2019s theorem, which considers the symmetric condition about the functional, we get infinitely many solutions; if f(x,u) is superlinear, using the symmetric mountain-pass theorem, infinitely many solutions can be obtained.<\/jats:p>","DOI":"10.3390\/sym14122486","type":"journal-article","created":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T02:25:36Z","timestamp":1669256736000},"page":"2486","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Infinitely Many Solutions for the Fractional p&amp;q-Laplacian Problems in RN"],"prefix":"10.3390","volume":"14","author":[{"given":"Liyan","family":"Wang","sequence":"first","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Chi","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jihong","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7965-1348","authenticated-orcid":false,"given":"Bin","family":"Ge","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,23]]},"reference":[{"key":"ref_1","unstructured":"Aris, R. 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