论文标题
与两个耦合的伪相关的Hartree方程相关的约束最小化问题
A constrained minimization problem related to two coupled pseudo-relativistic Hartree equations
论文作者
论文摘要
我们关注以下约束最小化问题：$$ e（a_ {1}，a_ {2}，β）：= \ inf \ left \ left \ {e_ {a_ {1}，a_ {2}，β}，β}，β}（u_ {1}，u_ {2}，U_ {2}），U_ {2}）： \ | U_ {1} \ | _ {l^{2}（\ Mathbb {r}^{3}）} = \ | U_ {2} \ | _ {l^{2}} $ e_ {a_ {1}，a_ {2}，β} $是与两个耦合的伪偏移的hartree方程相关的能量功能，涉及三个参数$ a_ {1}，a_ {1}，a_ {2}，β$和两个诱捕潜力$ v_1（x）$ v_1 $ v_1 $和$ v_2（x）$ v_2（x）$ v_2（x2（x））$ v_2（x）。在本文中，我们获得了$ e（a_ {1}，a_ {2}，β）$的最小化，以$ a_ {1}，a_ {2} $和$β$在适当条件下的潜力条件下，这在不同的感觉上概括了[16,17,18]。
We are concerned with the following constrained minimization problem: $$e(a_{1},a_{2},β) := \inf\left\{E_{a_{1},a_{2},β}(u_{1},u_{2}): \|u_{1}\|_{L^{2}(\mathbb{R}^{3})} = \|u_{2}\|_{L^{2}(\mathbb{R}^{3})} = 1\right\},$$ where $E_{a_{1},a_{2},β}$ is the energy functional associated to two coupled pseudo-relativistic Hartree equations involving three parameters $a_{1}, a_{2}, β$ and two trapping potentials $V_1(x)$ and $V_2(x)$. In this paper, we obtain the existence of minimizers of $e(a_{1},a_{2},β)$ for possible $a_{1}, a_{2}$ and $β$ under suitable conditions on the potentials, which generalizes the results of the papers [16,17,18] in different senses.
