{"title":"用变分法求解一类分数阶半线性方程","authors":"R. Karki","doi":"10.5206/mase/9413","DOIUrl":null,"url":null,"abstract":"We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A solution to a fractional order semilinear equation using variational method\",\"authors\":\"R. Karki\",\"doi\":\"10.5206/mase/9413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation.\",\"PeriodicalId\":93797,\"journal\":{\"name\":\"Mathematics in applied sciences and engineering\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in applied sciences and engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mase/9413\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/9413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A solution to a fractional order semilinear equation using variational method
We will discuss how we obtain a solution to a semilinear pseudo-differential equation involving fractional power of laplacian by using a method analogous to the direct method of calculus of variations. More precisely, we will discuss the existence of a minimizer of a suitable energy type functional whose Euler-Lagrange equation is the given semilinear pseudo-differential equation, and also discuss the regularity of such a minimizer so that it will be a solution to the semilinear equation.
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