Abstract
We discuss nonlinear eigenvalue boundary value problems arising in nonlinear fracture mechanics due to determination of the stress-strain state in the vicinity of the crack tip in power law hardening or creep power law materials. The study is aimed at analytical determination of eigenfunctions and eigen values of the nonlinear eigenvalue problems following from the problem of determining the crack tip fields at crack in power law materials under Mode III, Mode I, Mode II and Mixed Mode loadings. The study is based on the perturbation theory technique (small artificial parameter method) allowing us to find the analytical solution for the eigenvalues in the approximate form. The method of analytical determination of eigenfunctions of the problem is presented.
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