This paper is concerned with the following biharmonic problem {Δ2u=|u|8N−4uin  Ω∖B(ξ0,ε)―,u=Δu=0on  ∂(Ω∖B(ξ0,ε)―), where Ω is an open bounded domain in RN , N⩾5 , and B(ξ0,ε) is a ball centered at ξ ₀ with radius ɛ, ɛ is a small positive parameter. We obtain the existence of solutions for problem (0.1), which is an arbitrary large number of sign-changing solutions whose profile is a superposition of bubbles with alternate sign which concentrate at the centre of the hole.

中文翻译：

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针对帕尼茨型问题的符号改变气泡塔解决方案

本文关注以下双调和问题 {Δ2你=|你|8氮-4你在  Ω∖乙（Ψ0,ε）―,你=Δ你=0在  ∂（Ω∖乙（Ψ0,ε）―）, 其中 Ω 是开有界域 右氮 , 氮⩾5 ， 和 乙（Ψ0,ε） 是一个以Ψ ₀半径ε,ε是一个小的正参数。我们得到了问题(0.1)解的存在性，它是任意大量的变号解，其轮廓是集中在孔中心的具有交替符号的气泡的叠加。