{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:55:29Z","timestamp":1760151329002,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T00:00:00Z","timestamp":1647475200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Agencia Estatal de Investigaci\u00f3n (AEI) of Spain","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}]},{"name":"European Community fund FEDER","award":["PID2020-113275GB-I00"],"award-info":[{"award-number":["PID2020-113275GB-I00"]}]},{"DOI":"10.13039\/501100010801","name":"Xunta de Galicia","doi-asserted-by":"publisher","award":["ED431C 2019\/02"],"award-info":[{"award-number":["ED431C 2019\/02"]}],"id":[{"id":"10.13039\/501100010801","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we were interested in obtaining the exact expression and studying the regions of constant sign of Green\u2019s function related to a second-order perturbed periodic problem coupled with integral boundary conditions at the extremes of the interval of the definition. To obtain the expression of Green\u2019s function related to this problem, we used the theory presented in a previous paper of the authors for general non-local perturbed boundary-value problems. Moreover, we characterized the parameter set where such a Green\u2019s function has a constant sign. To this end, we needed to consider first a related second-order problem without integral boundary conditions, obtaining the properties of its Green\u2019s function and then using them to compute the sign of the one related to the main problem.<\/jats:p>","DOI":"10.3390\/axioms11030139","type":"journal-article","created":{"date-parts":[[2022,3,20]],"date-time":"2022-03-20T21:25:00Z","timestamp":1647811500000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Constant-Sign Green\u2019s Function of a Second-Order Perturbed Periodic Problem"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1488-935X","authenticated-orcid":false,"given":"Alberto","family":"Cabada","sequence":"first","affiliation":[{"name":"Galician Centre For Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain"},{"name":"Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Facultade de Matem\u00e1ticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9167-0709","authenticated-orcid":false,"given":"Luc\u00eda","family":"L\u00f3pez-Somoza","sequence":"additional","affiliation":[{"name":"Galician Centre For Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain"},{"name":"Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Facultade de Matem\u00e1ticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7681-3652","authenticated-orcid":false,"given":"Mouhcine","family":"Yousfi","sequence":"additional","affiliation":[{"name":"Galician Centre For Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain"},{"name":"Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Facultade de Matem\u00e1ticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cabada, A. (2014). Green\u2019s Functions in the Theory of Ordinary Differential Equation, Springer. Springer Briefs in Mathematics.","DOI":"10.1007\/978-1-4614-9506-2"},{"key":"ref_2","unstructured":"Magnus, W., and Winkler, S. (1979). Hill\u2019s Equation, Dover Publications."},{"key":"ref_3","first-page":"6632236","article-title":"Existence of multiple solutions for second-order problem with Stieltjes integral boundary condition","volume":"2021","author":"Hu","year":"2021","journal-title":"J. Funct. 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Equ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5801","DOI":"10.3934\/math.2021343","article-title":"On a nonlinear mixed-order coupled fractional differential system with new integral boundary condition","volume":"6","author":"Ahmad","year":"2021","journal-title":"AIMS Math."},{"key":"ref_10","first-page":"1001","article-title":"On the existence and uniqueness of positive solutions for a p-Laplacian fractional boundary-value problem with an integral boundary condition with a parameter","volume":"9","author":"Ahmadkhanlu","year":"2021","journal-title":"Comput. Methods Differ. Equ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1186\/s13662-021-03225-y","article-title":"A fixed point approach to the solution of singular fractional differential equations with integral boundary conditions","volume":"2021","author":"Chandran","year":"2021","journal-title":"Adv. Differ. 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Mathematics, 9.","DOI":"10.3390\/math9161948"},{"key":"ref_15","first-page":"1","article-title":"The eigenvalue characterization for the constant sign Green\u2019s functions of (k,n-k) problems","volume":"44","author":"Cabada","year":"2016","journal-title":"Bound. Value Prob."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/3\/139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:38:02Z","timestamp":1760135882000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/3\/139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,17]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["axioms11030139"],"URL":"https:\/\/doi.org\/10.3390\/axioms11030139","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,3,17]]}}}