Ground state solutions and least energy sign-changing solutions for a class of fourth order Kirchhoff-type equations in

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• 作者：Sofiane Khoutir ^{sofiane_math@csu.edu.cn} ; Haibo Chen ; ^{math_chb@csu.edu.cn}
• 关键词：35J35 ; 35J40 ; 35J60
• 刊名：Arab Journal of Mathematical Sciences
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：94-108
• 全文大小：321 K
• 卷排序：23

文摘

In this article we study the problem Δ2u−(1+λ∫RN|∇u|2dx)Δu+V(x)u=|u|p−2uin RN, where Δ2≔Δ(Δ)Δ2≔Δ(Δ) is the biharmonic operator, λ>0λ>0 is a parameter, p∈(2,2∗)p∈(2,2∗), and V(x)∈C(RN,R)V(x)∈C(RN,R). Under appropriate assumptions on V(x)V(x), the existence of ground state solutions and a least energy sign-changing solution is obtained by combining the variational methods and the Nehari method.