| Abstract: |
| In this talk, we will consider the following $(p, q)$-Choquard equation
$\begin{equation*}
-\Delta_{p}u -\Delta_{q}u + |u|^{p-2}u + |u|^{q-2}u = \left(I_{\alpha}*F(u) \right) f(u) \quad \mbox{ in } \mathbb{R}^{N},
\end{equation*}$
where $2 \leq p$ < $q$ < $N$, $\Delta_{s}$ is the $s$--Laplacian operator with $s\in \{p, q\}$, $I_{\alpha}$ is the Riesz potential of order $\alpha \in \left( (N-2q)^{+}, N \right)$, $F\in C^{1}(\mathbb{R}, \mathbb{R})$ is a general nonlinearity of Berestycki--Lions type, and $F'=f$.
By means of variational methods, we analyze the existence of ground state solutions, along with the regularity, symmetry, and decay properties of these solutions. $\Delta_{s}$ is the $s$-Laplacian operator with $s\in \{p, q\}$, $I_{\alpha}$ is the Riesz potential of order $\alpha \in \left( (N-2q)^{+}, N \right)$, $F\in C^{1}(\mathbb{R}, \mathbb{R})$ is a general nonlinearity of Berestycki--Lions type, and $F'=f$.
By means of 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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