Localized eigenfunctions in the asymptotic model of the spectral problem

Localized eigenfunctions in the two-dimensional spectral problem containing a small parameter with higher derivatives are constructed on expected solution form. Localization this context means that exponentially decays both direc-tions starting from "weakest" point or line. The constructions based algo-rithm introduced by V.P. Maslov. A modification of algorithm for thin shell theory problems is given as an application. paper shows implementation to obtain formulas giving eigenvalues and corresponding eigenfunctions. An example solving specific given, illustrating stages applied asymptotic model.