论文标题
定期解决方案，可逆的二阶自动ddes在规定的对称非convex域中
Periodic Solutions to Reversible Second Order Autonomous DDEs in Prescribed Symmetric Nonconvex Domains
论文作者
论文摘要
使用BROUWER $ O（2）\ timesγ\ timesγ\ times \ MathBb Z_2 $ - 等级学位理论，研究了具有相应延迟的二阶可逆性自治系统的$2π$周期解决方案的存在和时空模式。该解决方案应该以规定的对称域$ d $进行其值，而$ o（2）$与逆转对称性与系统的自主形式相关。组$γ$反映了$ d $的对称性和/或在相应的相同振荡器网络中可能的耦合，$ \ Mathbb Z_2 $与右侧的奇数有关。基于$ \部分D $的高斯曲率，Hartman-Nagumo Type {\ IT先验边界}和Brouwer Equivariant度量技术的使用，抽象结果由$γ= d_8 $的具体示例支持 - d_8 $ - diheDral of dihedral of dehedral of loss $ 16 $ 16 $ 16 $。
The existence and spatio-temporal patterns of $2π$-periodic solutions to second order reversible equivariant autonomous systems with commensurate delays are studied using the Brouwer $O(2) \times Γ\times \mathbb Z_2$-equivariant degree theory. The solutions are supposed to take their values in a prescribed symmetric domain $D$, while $O(2)$ is related to the reversal symmetry combined with the autonomous form of the system. The group $Γ$ reflects symmetries of $D$ and/or possible coupling in the corresponding network of identical oscillators, and $\mathbb Z_2$ is related to the oddness of the right-hand side. Abstract results, based on the use of Gauss curvature of $\partial D$, Hartman-Nagumo type {\it a priori bounds} and Brouwer equivariant degree techniques, are supported by a concrete example with $Γ= D_8$ -- the dihedral group of order $16$.
