论文标题
在双曲线空间中存在一类椭圆方程的高能阳性溶液
Existence of high energy positive solutions for a class of elliptic equations in the hyperbolic space
论文作者
论文摘要
我们研究了双曲线空间上的以下标量字段问题的积极解决方案的存在， h^{1} {（\ Mathbb {b}^{n}）}，$$其中$ \ mathbb {b}^n $表示双曲线空间，$ 1 <p <2^* - 1：= \ frac {n+2} {n+2} {n-2} {n-2} { 1 <p <+\ infty $，如果$ n = 2，\;λ<\ frac {（n-1）^2} {4} $，以及$ 0 <in l^\ infty（\ mathbb {b}^n）。涉及相互作用的双曲气泡。
We study the existence of positive solutions for the following class of scalar field problem on the hyperbolic space $$ -Δ_{\mathbb{H}^N} u - λu = a(x) |u|^{p-1} \, u\;\;\text{in}\;\mathbb{B}^{N}, \quad u \in H^{1}{(\mathbb{B}^{N})}, $$ where $\mathbb{B}^N$ denotes the hyperbolic space, $1<p<2^*-1:=\frac{N+2}{N-2}$, if $N \geqslant 3; 1<p<+\infty$, if $N = 2,\;λ< \frac{(N-1)^2}{4}$, and $0< a\in L^\infty(\mathbb{B}^N).$ We prove the existence of a positive solution by introducing 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.
