{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:47:43Z","timestamp":1753886863014,"version":"3.41.2"},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,3,7]],"date-time":"2012-03-07T00:00:00Z","timestamp":1331078400000},"content-version":"vor","delay-in-days":66,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10971183"],"award-info":[{"award-number":["10971183"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"Using two successive reductions: B\u2010equivalence of the system on a variable time scale to a system on a time scale and a reduction to an impulsive differential equation and by Leggett\u2010Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equation on variable time scales with a transition condition between two consecutive parts of the scale , (t<\/jats:italic>, x<\/jats:italic>) \u2208 \ud835\udd4b<\/jats:italic>0<\/jats:sub>(x<\/jats:italic>),, , where and are parameters, \ud835\udd4b<\/jats:italic>0<\/jats:sub>(x<\/jats:italic>) is a variable time scale with (\u03c9<\/jats:italic>, p<\/jats:italic>)\u2010property, c<\/jats:italic>(t<\/jats:italic>), \u2009\u2009<\/jats:italic>a<\/jats:italic>(t<\/jats:italic>), v<\/jats:italic>j<\/jats:italic><\/jats:sub>(t<\/jats:italic>), and f<\/jats:italic>j<\/jats:italic><\/jats:sub>(t<\/jats:italic>, x<\/jats:italic>) \u2009\u2009<\/jats:italic>(j<\/jats:italic> = 1,2, \u2026, n<\/jats:italic>) are \u03c9<\/jats:italic>\u2010periodic functions of t<\/jats:italic>, B<\/jats:italic>i<\/jats:italic>+p<\/jats:italic><\/jats:sub> = B<\/jats:italic>i<\/jats:italic><\/jats:sub>, \u2009\u2009<\/jats:italic>J<\/jats:italic>i<\/jats:italic>+p<\/jats:italic><\/jats:sub>(x<\/jats:italic>) = J<\/jats:italic>i<\/jats:italic><\/jats:sub>(x<\/jats:italic>) uniformly with respect to i<\/jats:italic> \u2208 \u2124<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/2012\/516476","type":"journal-article","created":{"date-parts":[[2012,3,7]],"date-time":"2012-03-07T21:01:20Z","timestamp":1331154080000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales"],"prefix":"10.1155","volume":"2012","author":[{"given":"Yongkun","family":"Li","sequence":"first","affiliation":[]},{"given":"Chao","family":"Wang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,3,7]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2449-3"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00448-4"},{"key":"e_1_2_6_4_2","first-page":"185","article-title":"Stability of dynamic systems on the time scales","volume":"2","author":"Sivasundaram S.","year":"2002","journal-title":"Nonlinear Dynamics and Systems Theory"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2005.12.042"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2008.02.020"},{"key":"e_1_2_6_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2004.08.029"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2004.12.003"},{"key":"e_1_2_6_9_2","first-page":"1079","article-title":"The comparison method for differential equations with impulse action","volume":"26","author":"Akhmetov M. 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