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arXiv · 2604.04148

Existence and Concentration of Multiple Positive Solutions for a Logarithmic Fractional Schr\"odinger--Poisson System

Jiao Luo·Zhipeng Yang
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Abstract

We study a logarithmic fractional Schr\"odinger--Poisson system in \(\R^{3}\): \begin{equation*} \begin{cases} \varepsilon^{2\alpha}(-\Delta)^{\alpha}u+V(x)u+\phi u=u\log u^{2}+|u|^{p-2}u, & \text{in }\R^{3},\\ \varepsilon^{2\alpha}(-\Delta)^{\alpha}\phi=u^{2}, & \text{in }\R^{3}. \end{cases} \end{equation*} Here \(\alpha\in\bigl(\frac34,1\bigr)\), \(4 0\) and all sufficiently small \(\varepsilon>0\), the system admits at least \(\operatorname{cat}_{M_{\delta}}(M)\) distinct positive solutions. Moreover, the maximum points of these solutions concentrate near the global minimum set of \(V\) as \(\varepsilon\to0\).

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Jiao Luo, Zhipeng Yang. 2026-04-05. Existence and Concentration of Multiple Positive Solutions for a Logarithmic Fractional Schr\"odinger--Poisson System. https://arxiv.org/abs/2604.04148

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