| Abstract: |
| In this talk, we focus on the following class of $(p_{1}, p_{2})$-Laplacian problems:
$$\begin{equation*}
\left\{
\begin{array}{ll}
-\Delta_{p_{1}}u-\Delta_{p_{2}}u= g(u) \mbox{ in } \mathbb{R}^{N},
\
u\in W^{1, p_{1}}(\mathbb{R}^{N})\cap W^{1, p_{2}}(\mathbb{R}^{N}),
\end{array}
\right.
\end{equation*}$$
where $N\geq 2$, $1$<$p_{1}$<$p_{2}\leq N$, $\Delta_{p_{i}}$ is the $p_{i}$-Laplacian operator for $i=1, 2$, and $g:\mathbb{R}\to \mathbb{R}$ is a Berestycki-Lions type nonlinearity.
Using appropriate variational arguments, we obtain the existence of a ground state solution.
In particular, we provide three different approaches to deduce this result.
Finally, we prove the existence of infinitely many radially symmetric solutions. Our results improve and complement those that have appeared in the literature for this class of problems. |
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