论文标题
具有质量超临界非线性的Choquard方程的归一化解决方案
Normalized solutions for the Choquard equation with mass supercritical nonlinearity
论文作者
论文摘要
我们考虑非线性choquard方程$$ \ begin {cases}＆Δu=（i_α\ ast f（u））f'（u） \ int _ {\ mathbb {r}^n} | u |^2 dx = m，\ end {cases} $$，其中$α\ in（0，n）$，$ m> 0 $是处方的，$μ\ in \ mathbb {r} $是lagarange higarange fircliplier，是lagarange hive pieldiplier＆$i__α$ ies is is rieszz。 根据对非线性$ f的一般假设，我们证明了归一化解决方案的存在和多重性。
We consider the nonlinear Choquard equation $$\begin{cases} & - Δu = (I_α\ast F(u))F'(u) -μu \ \text{in}\ \mathbb{R}^N, & u \in \ H^1(\mathbb{R}^N), \ \int_{\mathbb{R}^N} |u|^2 dx=m, \end{cases} $$ where $α\in(0,N)$, $m>0$ is prescribed, $μ\in \mathbb{R}$ is a Lagarange multiplier, and $I_α$ is the Riesz potential. Under general assumptions on the nonlinearity $F,$ we prove the existence and multiplicity of normalized solutions.
