{"title":"The Sign-Changing Solution for Fractional (p,q)-Laplacian Problems Involving Supercritical Exponent","authors":"Jianwen Zhou, Chengwen Gong, Wenbo Wang","doi":"10.3390/fractalfract8040186","DOIUrl":null,"url":null,"abstract":"In this article, we consider the following fractional (p,q)-Laplacian problem (−Δ)ps1u+(−Δ)qs2u+V(x)(|u|p−2u+|u|q−2u)=f(u)+λ|u|r−2u, where x∈RN, (−Δ)ps1 is the fractional p-Laplacian operator ((−Δ)qs2 is similar), 0<s1<s2<1<p<q<Ns2, qs2*=NqN−s2q, r≥qs2*, f is a C1 real function and V is a coercive function. By using variational methods, we prove that the above problem admits a sign-changing solution if λ>0 is small.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":" 10","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractal and Fractional","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/fractalfract8040186","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we consider the following fractional (p,q)-Laplacian problem (−Δ)ps1u+(−Δ)qs2u+V(x)(|u|p−2u+|u|q−2u)=f(u)+λ|u|r−2u, where x∈RN, (−Δ)ps1 is the fractional p-Laplacian operator ((−Δ)qs2 is similar), 00 is small.
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