论文标题
部分可观测时空混沌系统的无模型预测
Normalized solutions for Schrödinger-Bopp-Podolsky system
论文作者
论文摘要
在本文中，我们研究以下能量功能源自Schrödinger-Bopp-Podolsky System $$ i（u）= \ frac {1} {2} {2} \ int _ {\ Mathbb {r} u |^{2} dx+\ frac {1} {4} \ int _ {\ mathbb {r}^{3}}} ϕ_ { h^{1}（\ Mathbb {r}^{3}，c）：\ \ \ weled \ | u \ right \ right \ | _ {2} =ρ\ right \}，$ $ρ> 0。使用最小化方法获取归一化解决方案。
In this paper, we study the following energy functional originates from the Schrödinger-Bopp-Podolsky system $$I(u)=\frac{1}{2}\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx+\frac{1}{4}\int_{\mathbb{R}^{3}} ϕ_{u}u^{2}dx-\frac{1}{p}\int_{\mathbb{R}^{3}}|u|^{p}dx$$ constrained on $B_ρ=\left\{u\in H^{1}(\mathbb{R}^{3},C):\ \left\|u\right\|_{2}=ρ\right\},$ where $ρ>0.$ As such constrained problem $I(u)$ is bounded from below on $B_ρ$ when $p\in(2,\frac{10}{3}).$ We use minimizing method to get a normalized solution.
