{"title":"关于∧p B","authors":"J. Ereú, L. Pérez, Luz Rodríguez","doi":"10.1155/2022/5482688","DOIUrl":null,"url":null,"abstract":"<jats:p>In this paper, we define the space of functions <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <msub>\n <mi mathvariant=\"normal\">Λ</mi>\n <mrow>\n <mi>p</mi>\n </mrow>\n </msub>\n </math>\n </jats:inline-formula>-bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msub>\n <mi mathvariant=\"normal\">Λ</mi>\n <mrow>\n <mi>p</mi>\n </mrow>\n </msub>\n <mi>B</mi>\n <mi>V</mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <msubsup>\n <mi>I</mi>\n <mi>a</mi>\n <mi>b</mi>\n </msubsup>\n <mo>,</mo>\n <mi>ℝ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula>.</jats:p>","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"74 8","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <msub>\\n <mi>Λ</mi>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n </msub>\\n <mi>B</mi>\\n \",\"authors\":\"J. Ereú, L. Pérez, Luz Rodríguez\",\"doi\":\"10.1155/2022/5482688\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>In this paper, we define the space of functions <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <msub>\\n <mi mathvariant=\\\"normal\\\">Λ</mi>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n </msub>\\n </math>\\n </jats:inline-formula>-bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <msub>\\n <mi mathvariant=\\\"normal\\\">Λ</mi>\\n <mrow>\\n <mi>p</mi>\\n </mrow>\\n </msub>\\n <mi>B</mi>\\n <mi>V</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <msubsup>\\n <mi>I</mi>\\n <mi>a</mi>\\n <mi>b</mi>\\n </msubsup>\\n <mo>,</mo>\\n <mi>ℝ</mi>\\n </mrow>\\n </mfenced>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula>.</jats:p>\",\"PeriodicalId\":55967,\"journal\":{\"name\":\"International Journal of Differential Equations\",\"volume\":\"74 8\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2022/5482688\",\"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":"International Journal of Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2022/5482688","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文在平面上定义了p有界变分函数空间Λ，并赋予其范数，使其为Banach空间。此外，我们研究了一些非线性积分方程，并给出了这些方程所涉及的函数和核的条件，在这些条件下，我们保证了平面上Shiba意义上有界变分函数在空间上的存在唯一性。Λ p B V IA b，和。
In this paper, we define the space of functions -bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, .
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