{"title":"关于空间K '中的一阶线性奇异微分方程","authors":"Abdourahman Haman Adji, Shankishvili Lamara Dmitrievna","doi":"10.59400/jam.v1i2.88","DOIUrl":null,"url":null,"abstract":"We propose in this work to describe all the generalized-function solutions of the non-homogeneous first-order linear singular differential equation with two real numbers, and , in the space of generalized functions K’. In the case of a second right-hand side consisting of an s-order derivative of the Dirac-delta function, we have completely investigated the considered equation when we look for the solution in the form of with the unknown coefficients which we have determined case by case, taking into account the relationship between the parameters inside. On the basis of what has been done, we focus our present research to apply the principle of superposition of the solutions that is conducting us to the awaited result when we also maintain the classical solutions of the homogeneous equation which remains the same.","PeriodicalId":495855,"journal":{"name":"Journal of AppliedMath","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a first order linear singular differential equation in the space K’\",\"authors\":\"Abdourahman Haman Adji, Shankishvili Lamara Dmitrievna\",\"doi\":\"10.59400/jam.v1i2.88\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose in this work to describe all the generalized-function solutions of the non-homogeneous first-order linear singular differential equation with two real numbers, and , in the space of generalized functions K’. In the case of a second right-hand side consisting of an s-order derivative of the Dirac-delta function, we have completely investigated the considered equation when we look for the solution in the form of with the unknown coefficients which we have determined case by case, taking into account the relationship between the parameters inside. On the basis of what has been done, we focus our present research to apply the principle of superposition of the solutions that is conducting us to the awaited result when we also maintain the classical solutions of the homogeneous equation which remains the same.\",\"PeriodicalId\":495855,\"journal\":{\"name\":\"Journal of AppliedMath\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of AppliedMath\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.59400/jam.v1i2.88\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of AppliedMath","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59400/jam.v1i2.88","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On a first order linear singular differential equation in the space K’
We propose in this work to describe all the generalized-function solutions of the non-homogeneous first-order linear singular differential equation with two real numbers, and , in the space of generalized functions K’. In the case of a second right-hand side consisting of an s-order derivative of the Dirac-delta function, we have completely investigated the considered equation when we look for the solution in the form of with the unknown coefficients which we have determined case by case, taking into account the relationship between the parameters inside. On the basis of what has been done, we focus our present research to apply the principle of superposition of the solutions that is conducting us to the awaited result when we also maintain the classical solutions of the homogeneous equation which remains the same.