二阶高级差分方程的修正振动结果

J. Appl. Math. Pub Date : 2022-06-30 DOI:10.1155/2022/3407776

G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani

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Thandapani","doi":"10.1155/2022/3407776","DOIUrl":null,"url":null,"abstract":"In this paper, we present a new method to establish the oscillation of advanced second-order difference equations of the form \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>Δ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>η</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>Δ</mi>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n <mo>+</mo>\n <mi>ρ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>σ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n <mo>=</mo>\n <mn>0</mn>\n <mo>,</mo>\n </math>\n using the ordinary difference equation \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>Δ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>η</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>Δ</mi>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n <mo>+</mo>\n <mi>q</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </mfenced>\n <mo>=</mo>\n <mn>0</mn>\n <mo>.</mo>\n </math>\n The obtained results are new and improve the existing criteria. We provide examples to illustrate the main results.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"11 1","pages":"3407776:1-3407776:5"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modified Oscillation Results for Advanced Difference Equations of Second-Order\",\"authors\":\"G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani\",\"doi\":\"10.1155/2022/3407776\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a new method to establish the oscillation of advanced second-order difference equations of the form \\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>Δ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>η</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n <mi>Δ</mi>\\n <mi>υ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n </mrow>\\n </mfenced>\\n <mo>+</mo>\\n <mi>ρ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n <mi>υ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>σ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n </mrow>\\n </mfenced>\\n <mo>=</mo>\\n <mn>0</mn>\\n <mo>,</mo>\\n </math>\\n using the ordinary difference equation \\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>Δ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>η</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n <mi>Δ</mi>\\n <mi>υ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n </mrow>\\n </mfenced>\\n <mo>+</mo>\\n <mi>q</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n </mrow>\\n </mfenced>\\n <mi>υ</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\">\\n <mrow>\\n <mi>ℓ</mi>\\n <mo>+</mo>\\n <mn>1</mn>\\n </mrow>\\n </mfenced>\\n <mo>=</mo>\\n <mn>0</mn>\\n <mo>.</mo>\\n </math>\\n The obtained results are new and improve the existing criteria. We provide examples to illustrate the main results.\",\"PeriodicalId\":14766,\"journal\":{\"name\":\"J. Appl. Math.\",\"volume\":\"11 1\",\"pages\":\"3407776:1-3407776:5\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"J. Appl. Math.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2022/3407776\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Appl. 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