{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:08:26Z","timestamp":1760231306675,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,5]],"date-time":"2022-09-05T00:00:00Z","timestamp":1662336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971126","IRT 16R16"],"award-info":[{"award-number":["11971126","IRT 16R16"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Program for Changjiang Scholars and Innovative Research Team in University","award":["11971126","IRT 16R16"],"award-info":[{"award-number":["11971126","IRT 16R16"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we study the existence and multiplicity of solutions for the discrete Dirichlet boundary value problem of the Kirchhoff type, which has a symmetric structure. By using the critical point theory, we establish the existence of infinitely many solutions under appropriate assumptions on the nonlinear term. Moreover, we obtain the existence of infinitely many positive solutions via the strong maximum principle. Finally, we take two examples to verify our results.<\/jats:p>","DOI":"10.3390\/sym14091844","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T09:51:09Z","timestamp":1662630669000},"page":"1844","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Infinitely Many Solutions for the Discrete Boundary Value Problems of the Kirchhoff Type"],"prefix":"10.3390","volume":"14","author":[{"given":"Weihua","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China"},{"name":"Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhan","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China"},{"name":"Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1137\/20M1368367","article-title":"Modeling and analysis of the implementation of the Wolbachia incompatible and sterile insect technique for mosquito population suppression","volume":"81","author":"Zheng","year":"2021","journal-title":"SIAM J. 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