一类带 Hardy 项的 Choquard 方程的全局紧性结果——献给邓引斌教授 70 寿辰

Abstract

Abstract:

In this paper, we deal with a Choquard-type equation with Hardy potential

$ \begin{cases} -\Delta u-\lambda u-\mu\displaystyle\frac{u}{|x|^2}=\bigl(I_\alpha* | u|^{\bar p}\bigr)|u |^{{\bar p}-2}u+f(x,u),\\ u\in H^1_0(\Omega), \end{cases} $

where $N\geq 3, 0 < \mu < \dfrac{(N-2)^{2}}{4}$, $\Omega\subset\mathbb{R}^N$ is a bounded domain, $\bar{p}= \dfrac{N+\alpha}{N-2}$ is the upper critical exponent of Hardy-Littlewood-Sobolev inequality. Through a compactness analysis of the functional corresponding to the above equation, we obtain the existence of positive solutions.

Key words: compactness, Sobolev-Hardy inequality, Choquard-type equation, critical exponent

CLC Number:

O175.2

Lingyu Jin, Suting Wei. A Global Compact Result for a Choquard-Type Equation with Hardy Potential[J].Acta mathematica scientia,Series A, 2026, 46(4): 1471-1485.

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A Global Compact Result for a Choquard-Type Equation with Hardy Potential

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