| Abstract: |
| In this talk, we will consider the following fractional Choquard--Kirchhoff equation
$$\begin{equation*}
\left(a+b\iint_{\mathbb{R}^{2N}} \frac{|u(x)- u(y)|^{2}}{|x-y|^{N+2s}} \, dxdy \right) (-\Delta)^{s} u + u = \left(I_{\alpha}*F(u) \right) F`(u) \quad \mbox{ in } \mathbb{R}^{N},
\end{equation*}$$
where $N\geq 2$, $a, b>0$ are constants, $(-\Delta)^{s}$ is the fractional Laplacian operator of order $s\in (0,1)$, $I_{\alpha}$ is the Riesz potential of order $\alpha \in \left( (N-4s)^{+}, N \right)$, $F\in C^{1}(\mathbb{R}, \mathbb{R})$ is a general nonlinearity of Berestycki--Lions type. Applying suitable variational methods, we analyze the existence of ground state solutions, along with the regularity, symmetry, and decay properties of these solutions. |
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