{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:49:06Z","timestamp":1765212546303,"version":"3.46.0"},"reference-count":19,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T00:00:00Z","timestamp":1764460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Umm Al-Qura University, Saudi Arabia","award":["25UQU4331214GSSR12"],"award-info":[{"award-number":["25UQU4331214GSSR12"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We establish the existence and uniqueness of solutions to a class of second-order nonlinear boundary value problems involving impulses, delay, and possible singularities. The approach leverages the recent notion of paired-Chatterjea-type contractions. Under a smallness condition ensuring the associated integral operator is a Banach contraction with constant \u03bc&lt;13, we show that it is also a Chatterjea, and hence, a paired-Chatterjea contraction. By the fixed point theorem of Chand, this guarantees at most two fixed points; a supplementary uniqueness argument then ensures a unique solution in the Banach space PC1([a,b]).<\/jats:p>","DOI":"10.3390\/axioms14120891","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:41:41Z","timestamp":1765212101000},"page":"891","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Uniqueness of Solutions to Singular Impulsive Delay Boundary Value Problems via Paired-Chatterjea-Type Contractions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-2071","authenticated-orcid":false,"given":"Nicola","family":"Fabiano","sequence":"first","affiliation":[{"name":"\u201cVin\u010da\u201d Institute of Nuclear Sciences-National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2430-6499","authenticated-orcid":false,"given":"Zouaoui","family":"Bekri","sequence":"additional","affiliation":[{"name":"Laboratory of Fundamental and Applied Mathematics, University of Oran 1, Ahmed Ben Bella, Es-Senia 31000, Algeria"},{"name":"Department of Sciences and Technology, Institute of Sciences, Nour-Bachir University Center, El-Bayadh 32000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6652-5868","authenticated-orcid":false,"given":"Amir","family":"Baklouti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Sfax University, Sfax 3029, Tunisia"}]},{"given":"Saber","family":"Mansour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, P.O. Box 14035, Holy Makkah 21955, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1977). Theory of Functional Differential Equations, Springer.","DOI":"10.1007\/978-1-4612-9892-2"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lakshmikantham, V., Bainov, D.D., and Simeonov, P.S. (1989). Theory of Impulsive Differential Equations, World Scientific.","DOI":"10.1142\/0906"},{"key":"ref_3","first-page":"124714","article-title":"Impulsive delay differential equations and their applications in population dynamics","volume":"365","author":"Liu","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.jmaa.2003.10.005","article-title":"Continuous-time additive Hopfield-type neural networks with impulses","volume":"290","author":"Akca","year":"2004","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hale, J.K., and Verduyn Lunel, S.M. (1993). Introduction to Functional Differential Equations, Springer.","DOI":"10.1007\/978-1-4612-4342-7"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. Math."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Granas, A., and Dugundji, J. (2003). Fixed Point Theory, Springer.","DOI":"10.1007\/978-0-387-21593-8"},{"key":"ref_8","first-page":"71","article-title":"Some results on fixed points","volume":"60","author":"Kannan","year":"1968","journal-title":"Bull. Calcutta Math. Soc."},{"key":"ref_9","first-page":"794","article-title":"Fixed-point theorems","volume":"22","author":"Chatterjea","year":"1972","journal-title":"Czechoslov. 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Ordinary Differential Equations, SIAM.","DOI":"10.1137\/1.9780898719222"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/12\/891\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:44:27Z","timestamp":1765212267000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/12\/891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,30]]},"references-count":19,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["axioms14120891"],"URL":"https:\/\/doi.org\/10.3390\/axioms14120891","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,30]]}}}