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Abstract
We consider oscillations in cylindrical slotted resonators formed by combinations of rectangular domains with several slots cut in the walls using the methods of approximate semi-inversion of integral operator-valued functions with a logarithmic singularity of the kernel. The initial boundary value problems for the Helmholtz equation are reduced to Fredholm integral equations and systems of integral equations of the first kind with a logarithmic singularity. In the case of narrow slots, the dispersion equations are obtained and evaluated using perturbations and the small-parameter method. Eigenfrequencies and eigenfields are calculated explicitly. The values of geometrical and material parameters are determined that lead to the interaction of oscillations. The results obtained are used for improving the design of filters and switches on the basis of simple model prototype structures.