Asymptotic Properties of Parametric Eigenvalue Problems in a Hilbert space.

We study a parametric eigenvalue problem in an infinite-dimensional Hilbert space arising in the mechanics of loaded thin-walled structures. Asymptotic properties of solutions depending on the loading parameters are established. The initial infinite-dimensional problem is approximated in a finite-dimensional subspace. Theoretical error estimates of approximate solutions are obtained. Effective numerical methods for calculating the main resonance frequency and the corresponding resonance form of vibrations based on the asymptotic formulas are proposed. [ABSTRACT FROM AUTHOR]