The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N - 1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly general hypotheses, including the special case where the obstacles consist of line segments placed parallel to the waveguide walls. Copyright (C) 2004 John Wiley Sons, Ltd.
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机译：拉普拉斯算子被认为是受周期性结构干扰的波导，该周期性结构由跨越波导的N个全等障碍组成。诺伊曼边界条件施加在周期性结构上，诺伊曼或Dirichlet条件施加在导向壁上。事实证明，在相当笼统的假设下，包括特殊情况下，障碍物由平行于波导壁的线段组成，在Neumann情况（resich。Dirichlet情况）中，至少存在N个（respons。N-1）陷获模式。 。版权所有（C）2004 John Wiley Sons，Ltd.
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