| Abstract: |
| In this talk, I will discuss the following Poincare-Sobolev-type equation
$\begin{equation*}
-\Delta_{\mathbb{H}^N} u - \lambda u = a(x) |u|^{p-1} \, u\;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})},
\end{equation*}$
where $\mathbb{B}^N$ denotes the hyperbolic space, $16$ in the critical case, whereas in the subcritical case, we use the min-max procedure in the spirit of Bahri-Li in the hyperbolic space and using a series of new estimates involving interacting hyperbolic bubbles. |
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