{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:27:07Z","timestamp":1760236027579,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T00:00:00Z","timestamp":1634774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12061067"],"award-info":[{"award-number":["12061067"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the upper and lower solution method is proposed in order to solve the second order interval boundary value problem. We study first a class of linear interval boundary value problems and then investigate a class of nonlinear interval boundary value problems by the upper and lower solution method under the gH-derivative, and we prove that there exist at least two solutions.<\/jats:p>","DOI":"10.3390\/axioms10040269","type":"journal-article","created":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T14:37:48Z","timestamp":1634827068000},"page":"269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Upper and Lower Solution Method for a Class of Interval Boundary Value Problems"],"prefix":"10.3390","volume":"10","author":[{"given":"Yanzong","family":"Yan","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Longdong University, Qingyang 745000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8590-1021","authenticated-orcid":false,"given":"Zhiyong","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Longdong University, Qingyang 745000, China"}]},{"given":"Zengtai","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02265313","article-title":"Calculus for interval functions of real variable","volume":"22","author":"Markov","year":"1979","journal-title":"Computing"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Stefanini, L. 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Comput."},{"key":"ref_6","first-page":"1","article-title":"A new gH-difference for multi-dimensional convex sets and convex fuzzy sets","volume":"48","author":"Stefanini","year":"2019","journal-title":"Axioms"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Stefanini, L., Guerra, M.L., and Amicizia, B. (2019). Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable. Part I: Partial Orders, gH-Derivative, Monotonicity. Axioms, 8.","DOI":"10.3390\/axioms8040113"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Stefanini, L., Sorini, L., and Amicizia, B. (2019). Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable\u2014Part II: Extremal Points, Convexity, Periodicity. 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Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2016.09.015","article-title":"Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability","volume":"309","author":"Hoa","year":"2017","journal-title":"Fuzzy Sets Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.fss.2017.09.006","article-title":"Existence results for extremal solutions of interval fractional functional integro-differential equations","volume":"347","author":"Hoa","year":"2018","journal-title":"Fuzzy Sets Syst."},{"key":"ref_13","unstructured":"Ladde, G.S., Lakshmikantham, V., and Vatsala, A.S. (1985). Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2047","DOI":"10.1016\/j.fss.2007.12.020","article-title":"Monotone method for fuzzy differential equations","volume":"159","year":"2008","journal-title":"Fuzzy Sets Syst."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/269\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:20:27Z","timestamp":1760167227000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/269"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,21]]},"references-count":14,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["axioms10040269"],"URL":"https:\/\/doi.org\/10.3390\/axioms10040269","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,10,21]]}}}