论文标题
在方程右侧和边界条件的多项式的层中，helmholtz方程的边界值问题的确切解决方案的确切解决方案
Exact solutions of the boundary-value problems for the Helmholtz equation in a layer with polynomials in the right-hand sides of the equation and of the boundary conditions
论文作者
论文摘要
在由两个超透明层界定的多维无限层中，考虑了具有多项式右侧的不均匀Helmholtz方程。结果表明，边界条件右侧的多项式和多项式的dirichlet和dirichlet-neumann边界值问题具有一种溶液，该解决方案是一种级别分析式，除了功率函数外，还包含功能函数，还具有夸张或三角函数。如果方程的参数不是特征值，则该解决方案在缓慢生长功能类别中是唯一的。给出了用于构建此解决方案的算法，并考虑了示例。
In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with polynomials in the right-hand sides of the boundary conditions have a solution that is a quasipolynomial that contains, in addition to the power functions, also hyperbolic or trigonometric functions. This solution is unique in the class of slow growth functions if the parameter of the equation is not an eigenvalue. An algorithm for constructing this solution is given and examples are considered.
