{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T22:54:59Z","timestamp":1772664899241,"version":"3.50.1"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T00:00:00Z","timestamp":1456790400000},"content-version":"unspecified","delay-in-days":60,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>Consider the first-order retarded differential equation<jats:disp-formula id=\"S1461157016000073_eqnU1\"><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_eqnU1\"\/><jats:tex-math>$$\\begin{eqnarray}x^{\\prime }(t)+p(t)x({\\it\\tau}(t))=0,\\quad t\\geqslant t_{0},\\end{eqnarray}$$<\/jats:tex-math><\/jats:alternatives><\/jats:disp-formula>where<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_inline1\"\/><jats:tex-math>$p(t)\\geqslant 0$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_inline2\"\/><jats:tex-math>${\\it\\tau}(t)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is a function of positive real numbers such that<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_inline3\"\/><jats:tex-math>${\\it\\tau}(t)\\leqslant t$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>for<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_inline4\"\/><jats:tex-math>$t\\geqslant t_{0}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_inline5\"\/><jats:tex-math>$\\lim _{t\\rightarrow \\infty }{\\it\\tau}(t)=\\infty$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Under the assumption that the retarded argument is non-monotone, a new oscillation criterion, involving<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_inline6\"\/><jats:tex-math>$\\liminf$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, is established when the well-known oscillation condition<jats:disp-formula id=\"S1461157016000073_eqnU2\"><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1461157016000073_eqnU2\"\/><jats:tex-math>$$\\begin{eqnarray}\\liminf _{t\\rightarrow \\infty }\\int _{{\\it\\tau}(t)}^{t}p(s)\\,ds&gt;\\frac{1}{e}\\end{eqnarray}$$<\/jats:tex-math><\/jats:alternatives><\/jats:disp-formula>is not satisfied. An example illustrating the result is also given.<\/jats:p>","DOI":"10.1112\/s1461157016000073","type":"journal-article","created":{"date-parts":[[2016,3,14]],"date-time":"2016-03-14T10:38:06Z","timestamp":1457951886000},"page":"98-104","source":"Crossref","is-referenced-by-count":3,"title":["Oscillation of differential equations with non-monotone retarded arguments"],"prefix":"10.1112","volume":"19","author":[{"given":"George E.","family":"Chatzarakis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00d6zkan","family":"\u00d6calan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2016,3,1]]},"reference":[{"key":"S1461157016000073_r13","first-page":"1463","article-title":"Oscillating and monotone solutions of first-order differential equations with deviating arguments","volume":"8","author":"Koplatadze","year":"1982","journal-title":"Differ. 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