Existence of nontrivial solutions for a biharmonic equation with -Laplacian and singular sign-changing potential

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• 作者：Juntao Sun^a ; ^{sunjuntao2008@163.com} ; Tsung-fang Wu^b ; ^{tfwu@nuk.edu.tw}
• 关键词：Biharmonic equations ; Gagliardo&ndash ; Nirenberg inequality ; Hardy&ndash ; Sobolev inequality
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：66
• 期：Complete
• 页码：61-67
• 全文大小：762 K
• 卷排序：66

文摘

In the paper, we study a class of biharmonic equations with pp-Laplacian and singular sign-changing potential as follows: Δ2u−βΔpu+Vλ(x)u=0 in RN,u∈H2(RN),where N≥5N≥5, β<0β<0, Δpu=div(|∇u|p−2∇u)Δpu=div(|∇u|p−2∇u) with p≥2p≥2 and Vλ(x)=λa(x)−b(x)Vλ(x)=λa(x)−b(x) with λ>0λ>0. Under some suitable assumptions on aa and bb, we obtain the existence of nontrivial solutions for λλ large enough.