一类非线性Choquard方程基态解的存在性

Abstract

Abstract:

In this paper we study the following nonlinear Choquard equation $ \begin{equation} -\Delta u + V(x)u= (I_{\alpha}* F(u))f(u), \hskip0.5cm x\in{{\Bbb R}} ^{N} ,\end{equation} $ where $N \geq 3$, $\alpha \in (0, N)$, $I_{\alpha}$ is the Riesz potential, $V(x):\mathbb{R} ^{N} \rightarrow \mathbb{R} $ is a given potential function, and $F\in {\cal C}^{1}(\mathbb{R}, \mathbb{R})$ with $F'(s)=f(s)$. Under assumptions on $V$ and $f$, we do not require the $(AR)$ condition of $f$, the existence of ground state solutions are obtained via variational methods.

Key words: Choquard equation, Ground state solution, Variational methods

CLC Number:

O175.2

Xudong Shang,Jihui Zhang. Existence of Positive Ground State Solutions for the Choquard Equation[J].Acta mathematica scientia,Series A, 2022, 42(3): 749-759.

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References 28

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Existence of Positive Ground State Solutions for the Choquard Equation

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