Abstract:In this article, we consider the following problem:
\begin{align*}
-\Delta_{\mathbb{B}^N} u \, - \, \lambda u = |u|^{p-1}u, \quad u \in H^{1}(\mathbb{B}^N),
\end{align*}
where $N \geq 3$, $\lambda > \frac{N(N-2)}{4}$, and $1 < p \leq 2^*-1$. Here, $\mathbb{B}^N$ represents the Poincaré ball model of the hyperbolic space and $H^{1}(\mathbb{B}^N)$ denotes the Sobolev space on $\mathbb{B}^N$. In this work, we establish the existence and multiplicity of nonradial sign-changing solutions when $\lambda < \frac{(N-1)^2}{4}$, and $p = 2^*-1$. We also prove a partial non-existence result for a large class of symmetric solutions when $\lambda > \frac{(N-1)^2}{4}$.
From: Atanu Manna [view email]
[v1]
Wed, 24 Jun 2026 10:51:33 UTC (37 KB)
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