论文标题
关于分数brezis nirenberg类型方程的多种解决方案
On the existence of multiple solutions for fractional Brezis Nirenberg type equations
论文作者
论文摘要
本文在[4]中研究了著名的布雷兹和尼伦贝格的非本地分数类似物。也就是说，我们关注以下模型，$$ \ begin {align*} \ left（\ Mathcal {p} \ right）\ begin {cases} \ left（-Δ\ right）^s u-λu＆=α| ω，\\ u＆= 0 \ quad \ mbox {in} \ quad \ m \ mathbb {r}^n \setMinusΩ，\ end end {cases} \ end {align*} $（ - $（ - δ）$（ - δ）$是分数的laplace ocerator，$ s $ s $ s $ n $ s \ in（0,1,1） $ 2 <p <2^*$，$β> 0，λ，α\ in \ mathbb {r} $，并为问题$（\ mathcal {p}）$建立了非平凡解决方案和签名解决方案的存在。
The present paper studies the non-local fractional analogue of the famous paper of Brezis and Nirenberg in [4]. Namely, we focus on the following model, $$\begin{align*}\left(\mathcal{P}\right) \begin{cases} \left(-Δ\right)^s u-λu &= α|u|^{p-2}u + β|u|^{2^*-2}u \quad\mbox{in}\quad Ω,\\ u&=0\quad\mbox{in}\quad\mathbb{R}^N\setminusΩ, \end{cases} \end{align*}$$ where $(-Δ)^s$ is the fractional Laplace operator, $s \in (0,1)$, with $N \geq 3s$, $2<p<2^*$, $β>0, λ, α\in \mathbb{R}$ and establish the existence of nontrivial solutions and sign-changing solutions for the problem $(\mathcal{P})$.
