In this paper, we study the multiplicity of two spikes nodal solutions for a nonautonomous Schrödinger–Poisson system with the nonlinearity $ f(x)\vert u\vert ^{p-2}u(2<p<6) $ in $ \mathbb{R}^{3} $. By assuming that the weight function $ f\in C(\mathbb{R}^{3},\mathbb{R}^{+}) $ has $ m $ maximum points in $ \mathbb{R}^{3} $, we conclude that such system admits $ m^{2} $ distinct nodal solutions, each of which has exactly two nodal domains. The proof is based on a natural constraint approach developed by us as well as the generalized barycenter map.

中文翻译：

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权函数作用下Schrödinger-Poisson系统的节点解数

在本文中，我们研究了具有非线性$ f（x）\ vert u \ vert ^ {p-2} u（2 <p <6）$的非自治Schrödinger-Poisson系统的两个尖峰节点解的多重性\ mathbb {R} ^ {3} $。通过假设权重函数$ f \ in C（\ mathbb {R} ^ {3}，\ mathbb {R} ^ {+}）$在$ \ mathbb {R} ^ {3}中具有$ m $个最高点，我们得出结论，这样的系统接受$ m ^ {2} $个不同的节点解，每个节点解都恰好具有两个节点域。该证明基于我们开发的自然约束方法以及广义重心图。