| Abstract: |
| We devote this talk to discussing separation phenomena of radial solutions to the following Lane-Emden equation on the hyperbolic space $\mathbb{H}^{N}$:
\begin{align*}
-\Delta_{\mH^{N}} u=|u|^{p-1}u\quad\text{in}\quad\mathbb{H}^{N}.\tag{L}
\end{align*}
Regarding the equation (L), it is already known that for any exponent $p>1$, if the values of radial solutions at the origin are small enough, then a family of the radial solutions has separation property, i.e., any two radial solutions of the family do not intersect each other. In this talk, without the assumption of boundedness of radial solutions, we shall study separation phenomena of radial solutions to (L). Moreover, we also discuss the existence of a critical exponent with respect to separation phenomena of radial solutions to (L). |
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