We consider the following (p,q)-Laplacian Kirchhoff type problem −(a+b∫R3|∇u|pdx)Δpu−(c+d∫R3|∇u|qdx)Δqu+V(x)(|u|p−2u+|u|q−2u)=K(x)f(u)in R3, where a,b,c,d>0 are constants, 32<p<q<3, V:R3→R and K:R3→R are positive continuous functions allowed for vanishing behavior at infinity, and f is a continuous function with quasicritical growth. Using a minimization argument and a quantitative deformation lemma we establish the existence of nodal solutions.

中文翻译：

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势消失的双相基尔霍夫问题的节点解

我们考虑以下（p，q）-拉普拉斯基希霍夫型问题-（a +b∫R3|∇u| pdx）Δpu-（c +d∫R3|∇u| qdx）Δqu+ V（x）（| u | p-2u + | u | q-2u）= R3中的K（x）f（u），其中a，b，c，d> 0是常数，32 <p <q <3，V：R3→R和K：R3→R是允许在无穷大时消失的正连续函数，而f是具有准临界增长的连续函数。使用最小化参数和定量变形引理，我们建立了节点解的存在性。