论文标题
在具有关键指数增长的奇异哈密顿式椭圆形系统上
On a class of singular Hamiltonian Choquard-type elliptic systems with critical exponential growth
论文作者
论文摘要
在本文中，我们研究以下涉及单数重量\ BEGIN {EQNARRAY*}的Hamiltonian Choquard型椭圆形系统 \ begin {Aligned} \ DisplayStyle \ left \ {\ arraycolsep = 1.5pt \ begin {array} {ll} -ΔU + v（x）u = \ big（i_ {μ_{1}}} \ ast \ frac {g（v）} {| x | x |^α} \ big）\ frac {g（v）} \ Mathbb {r}^{2}，\\ [2mm] -ΔV + v（x）v = \ big（i_ {μ_{2}} \ ast \ frac {f（u）} {| x | x |^β} \ big）\ big）\ frac {f（u）} {| x | x |^β} \ end {array} \正确的。 \ end {Aligned} \ end {eqnarray*}其中$μ_{1}，μ_{2} \ in（0,2）$，$ 0 <α\ leq \ leq \ frac {μ__{μ_{1}}}} $V(x)$ is a continuous positive potential, $I_{μ_{1}}$ and $I_{μ_{2}}$ denote the Riesz potential, $\ast$ indicates the convolution operator, $F(s),G(s)$ are the primitive of $f(s),g(s)$ with $f(s),g(s)$ have exponential growth in $ \ mathbb {r}^{2} $。使用链接定理和变异方法，我们确定了上述问题的解决方案。
In this paper, we study the following Hamiltonian Choquard-type elliptic systems involving singular weights \begin{eqnarray*} \begin{aligned}\displaystyle \left\{ \arraycolsep=1.5pt \begin{array}{ll} -Δu + V(x)u = \Big(I_{μ_{1}}\ast \frac{G(v)}{|x|^α}\Big)\frac{g(v)}{|x|^α} \ \ \ & \mbox{in} \ \mathbb{R}^{2},\\[2mm] -Δv + V(x)v = \Big(I_{μ_{2}}\ast \frac{F(u)}{|x|^β}\Big)\frac{f(u)}{|x|^β} \ \ \ & \mbox{in} \ \mathbb{R}^{2}, \end{array} \right. \end{aligned} \end{eqnarray*} where $μ_{1},μ_{2}\in(0,2)$, $0<α\leq \frac{μ_{1}}{2}$, $0<β\leq \frac{μ_{2}}{2}$, $V(x)$ is a continuous positive potential, $I_{μ_{1}}$ and $I_{μ_{2}}$ denote the Riesz potential, $\ast$ indicates the convolution operator, $F(s),G(s)$ are the primitive of $f(s),g(s)$ with $f(s),g(s)$ have exponential growth in $\mathbb{R}^{2}$. Using the linking theorem and variational methods, we establish the existence of solutions to the above problem.
