论文标题
非radial解决方案的模式，用于轴上耦合半线性椭圆系统的模式
Patterns of Non-Radial Solutions to Coupled Semilinear Elliptic Systems on a Disc
论文作者
论文摘要
在本文中，我们证明了问题$ - \ triangle u = f（z，u）$，$ u | _ {\ partial d} = 0 $ in Tips disc $ d：= \ {z \ in \ mathbb c：| z | e | <1 \ f in $ f^k $ f^k $ f^k y in o o f（z \ n p^k）功能，相对于零$ $在零和满足$ f（e^{iθ} z，u），u）= f（z，u）$ in \ in \ mathbb r $，$ f（z，-u）= - f（z，z，u）$的满足$ u $。在假设$ f $尊重$ \ mathbb r^k $上的额外（空间）对称性的假设，我们研究了相应的非radial解决方案的对称属性。抽象结果由一个数字示例提供支持，其中包含额外的$ S_4 $ -symetries。
In this paper, we prove the existence of non-radial solutions to the problem $-\triangle u=f(z,u)$, $u|_{\partial D}=0$ on the unit disc $D:=\{z\in \mathbb C : |z|<1\}$ with $u(z)\in \mathbb R^k$, where $f$ is a sub-linear continuous function, differentiable with respect to $u$ at zero and satisfying $f(e^{iθ}z,u) = f(z,u)$ for all $θ\in \mathbb R$, $f(z,-u)=- f(z,u)$. Under the assumption that $f$ respects additional (spacial) symmetries on $\mathbb R^k$, we investigate symmetric properties of the corresponding non-radial solutions. The abstract result is supported by a numerical example with extra $S_4$-symmetries.
