论文标题
绿色的功能与山丘方程相关的关系与不同的边界价值条件相关
Relationship of the Green's functions related to the Hill's equation coupled to different boundary value conditions
论文作者
论文摘要
在本文中，我们将推断出与山丘方程相关的绿色功能的几种属性。特别是，这个想法是通过将绿色问题的绿色功能表示为其他问题的绿色功能的线性组合，研究与Neumann，Dirichlet，周期性和混合边界条件相连的二阶差速器操作员的绿色功能。这将使我们能够在持续符号时比较不同的绿色功能。最后，绿色线性问题功能的这种属性将是推断非线性问题解决方案的存在至关重要的。结果源自适用于在Banach空间中合适锥体上定义的相关操作员的固定点理论。
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential operator coupled to Neumann, Dirichlet, Periodic and Mixed boundary conditions, by expressing the Green's function of a given problem as a linear combination of the Green's function of the other ones. This will allow us to compare different Green's functions when they have constant sign. Finally, such properties of the Green's function of the linear problem will be fundamental to deduce the existence of solutions to the nonlinear problem. The results are derived from the fixed point theory applied to related operators defined on suitable cones in Banach spaces.
