Asymptotic solution of one-dimensional spectral boundary-value problems with rapidly varying coefficients: The case of multiple spectra

Abstract

We suggest a method for the construction of complete asymptotic expansions for eigenvalues and eigen-functions of spectral boundary-value problems for differential equations with rapidly varying coefficients in the case of multiple spectra of the averaged problem. The effect of splitting of multiple eigen-values is illustrated by an example of a special fourth-order problem.