{"title":"一类具有变号函数的分式问题解的存在性","authors":"F. M. Yaghoobi, J. Shamshiri","doi":"10.30495/JME.V15I0.2008","DOIUrl":null,"url":null,"abstract":"Here we study the existence and multiplicity of solutions for the following fractional problem $$ (-\\Delta)_p^s u+a(x) |u|^{p-2} u= f(x,u), $$ with the Dirichlet boundary condition $u=0$ on $\\partial\\Omega$ where $\\Omega$ is a bounded domain with smooth boundary, $p\\geq 2$, $s\\in(0,1)$ and $a(x)$ is a sign-changing function. Moreover, we consider two different assumptions on the function $f(x,u)$, including the cases of nonnegative and sign-changing function.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of solution for a class of fractional problems with sign-changing functions\",\"authors\":\"F. M. Yaghoobi, J. Shamshiri\",\"doi\":\"10.30495/JME.V15I0.2008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Here we study the existence and multiplicity of solutions for the following fractional problem $$ (-\\\\Delta)_p^s u+a(x) |u|^{p-2} u= f(x,u), $$ with the Dirichlet boundary condition $u=0$ on $\\\\partial\\\\Omega$ where $\\\\Omega$ is a bounded domain with smooth boundary, $p\\\\geq 2$, $s\\\\in(0,1)$ and $a(x)$ is a sign-changing function. Moreover, we consider two different assumptions on the function $f(x,u)$, including the cases of nonnegative and sign-changing function.\",\"PeriodicalId\":43745,\"journal\":{\"name\":\"Journal of Mathematical Extension\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Extension\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30495/JME.V15I0.2008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Extension","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30495/JME.V15I0.2008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence of solution for a class of fractional problems with sign-changing functions
Here we study the existence and multiplicity of solutions for the following fractional problem $$ (-\Delta)_p^s u+a(x) |u|^{p-2} u= f(x,u), $$ with the Dirichlet boundary condition $u=0$ on $\partial\Omega$ where $\Omega$ is a bounded domain with smooth boundary, $p\geq 2$, $s\in(0,1)$ and $a(x)$ is a sign-changing function. Moreover, we consider two different assumptions on the function $f(x,u)$, including the cases of nonnegative and sign-changing function.
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