{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:59:31Z","timestamp":1760230771667,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T00:00:00Z","timestamp":1659916800000},"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>This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of p(\u00b7)&amp;q(\u00b7)-Kirchhoff elliptic systems under Navier boundary conditions. By using the variational method and Ricceri\u2019s critical point theorem, we can find a proper conditions to ensure that the perturbed fourth-order of (p(x),q(x))-Kirchhoff systems has at least three weak solutions. We have extended and improved some recent results. The complexity of the combination of variable exponent theory and fourth-order Kirchhoff systems makes the results of this work novel and new contribution. Finally, a very concrete example is given to illustrate the applications of our results.<\/jats:p>","DOI":"10.3390\/sym14081630","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T09:47:06Z","timestamp":1660124826000},"page":"1630","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Class of Fourth-Order Symmetrical Kirchhoff Type Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Yong","family":"Wu","sequence":"first","affiliation":[{"name":"School of Tourism Data, Guilin Tourism University, Guilin 541006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Said","family":"Taarabti","sequence":"additional","affiliation":[{"name":"Information Systems and Technology Engineering Laboratory (LISTI), National School of Applied Sciences of Agadir, Ibn Zohr University, Agadir 80000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3146-6423","authenticated-orcid":false,"given":"Zakaria","family":"El Allali","sequence":"additional","affiliation":[{"name":"Team of Modeling and Scientific Computing Department of Mathematics, Multidisciplinary Faculty, Nador Mohammed First University, Oujda 6000, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khalil","family":"Ben Hadddouch","sequence":"additional","affiliation":[{"name":"National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Fez BP 2626, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5858-063X","authenticated-orcid":false,"given":"Jiabin","family":"Zuo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1063\/1.1698285","article-title":"Induced Fibration of Suspensions","volume":"20","author":"Winslow","year":"1949","journal-title":"J. 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