Yaşar Bolat , Murat Gevgeşoğlu , George E. Chatzarakis
{"title":"具有振荡系数的埃姆登-福勒型差分方程的振荡特性","authors":"Yaşar Bolat , Murat Gevgeşoğlu , George E. Chatzarakis","doi":"10.1016/j.rinam.2024.100472","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we give new criteria on the oscillation of the fourth-order Emden–Fowler type delay difference equation with oscillating coefficients of the form <span><span><span><math><mrow><mi>Δ</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>n</mi></mrow></msub><msubsup><mrow><mi>y</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>τ</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mo>=</mo><mn>0</mn><mtext>,</mtext><mi>n</mi><mo>≥</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mtext>,</mtext></mrow></math></span></span></span>where <span><math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mfenced><mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn></mrow></msup><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfenced></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> and <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>σ</mi></mrow></msub></mrow></math></span>. For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100472"},"PeriodicalIF":1.4000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000426/pdfft?md5=a75c766551a918235e26d7441f4c4d69&pid=1-s2.0-S2590037424000426-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Oscillatory properties for Emden–Fowler type difference equations with oscillating coefficients\",\"authors\":\"Yaşar Bolat , Murat Gevgeşoğlu , George E. Chatzarakis\",\"doi\":\"10.1016/j.rinam.2024.100472\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we give new criteria on the oscillation of the fourth-order Emden–Fowler type delay difference equation with oscillating coefficients of the form <span><span><span><math><mrow><mi>Δ</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>n</mi></mrow></msub><msubsup><mrow><mi>y</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>τ</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mo>=</mo><mn>0</mn><mtext>,</mtext><mi>n</mi><mo>≥</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mtext>,</mtext></mrow></math></span></span></span>where <span><math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mfenced><mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn></mrow></msup><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfenced></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> and <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>σ</mi></mrow></msub></mrow></math></span>. For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.</p></div>\",\"PeriodicalId\":36918,\"journal\":{\"name\":\"Results in Applied Mathematics\",\"volume\":\"23 \",\"pages\":\"Article 100472\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2590037424000426/pdfft?md5=a75c766551a918235e26d7441f4c4d69&pid=1-s2.0-S2590037424000426-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2590037424000426\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037424000426","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Oscillatory properties for Emden–Fowler type difference equations with oscillating coefficients
In this paper, we give new criteria on the oscillation of the fourth-order Emden–Fowler type delay difference equation with oscillating coefficients of the form where and . For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.
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