Geodesic
Eigenvalue analysis for a rack in a power-law material
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1399-1415

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A nonlinear eigenvalue problem related to determining the stress and strain fields near the tip of a transverse crack in a power-law material is studied. The eigenvalues are found by a perturbation method based on representations of an eigenvalue, the corresponding eigenfunction, and the material nonlinearity parameter in the form of series expansions in powers of a small parameter equal to the difference between the eigenvalues in the linear and nonlinear problems. The resulting eigenvalues are compared with the accurate numerical solution of the nonlinear eigenvalue problem. 
@article{ZVMMF_2009_49_8_a4,
     author = {L. V. Stepanova},
     title = {Eigenvalue analysis for a~rack in a~power-law material},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1399--1415},
     publisher = {mathdoc},
     volume = {49},
     number = {8},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a4/}
}
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L. V. Stepanova. Eigenvalue analysis for a rack in a power-law material. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1399-1415. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a4/