论文标题
存在针对一类分数的哈密顿型椭圆形系统的解决方案
Existence of solution for a class of fractional Hamiltonian-type elliptic systems with exponential critical growth in R
论文作者
论文摘要
在本文中，我们研究了以下类别的哈密顿系统：\ begin {eqnarray*} \ begin {Aligned} \ DisplayStyle \ left \ {\ arraycolsep = 1.5pt \ begin {array} {ll} （-Δ）^{\ frac {1} {2}} u + u = \ big（i_ {μ_{1}}} \ ast g（v）\ big）g（v） （-δ）^{\ frac {1} {2}} v + v = \ big（i_ {μ_{μ_{2}}} \ ast f（u）\ big）f（u） \ end {array} \正确的。 \ end {Aligned} \ end {eqnarray*}其中$（ - δ）^{\ frac {\ frac {1} {2}} $是平方根laplacian操作员，$μ__{1}，μ__{2} $I_{μ_{1}},I_{μ_{2}}$ 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 $\mathbb{R}$.使用链接定理和变异方法，我们建立了至少对上述问题的积极解决方案的存在。
In this paper, we study the following class of fractional Hamiltonian systems: \begin{eqnarray*} \begin{aligned}\displaystyle \left\{ \arraycolsep=1.5pt \begin{array}{ll} (-Δ)^{\frac{1}{2}} u + u = \Big(I_{μ_{1}}\ast G(v)\Big)g(v) \ \ \ & \mbox{in} \ \mathbb{R},\\[2mm] (-Δ)^{\frac{1}{2}} v + v = \Big(I_{μ_{2}}\ast F(u)\Big)f(u) \ \ \ & \mbox{in} \ \mathbb{R}, \end{array} \right. \end{aligned} \end{eqnarray*} where $(-Δ)^{\frac{1}{2}}$ is the square root Laplacian operator, $μ_{1},μ_{2}\in(0,1)$, $I_{μ_{1}},I_{μ_{2}}$ 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 $\mathbb{R}$. Using the linking theorem and variational methods, we establish the existence of at least one positive solution to the above problem.
