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-The stability of implicit difference scheme for parabolic equations subject to integral conditions, which correspond to the quasi-static flexure of a thermoelastic rod is considered. The stability analysis is based on the spectral structure of matrix of the difference scheme. The stability conditions obtained here differ from those presented in the articles of other authors.2000 Mathematics Subject Classification: 65M06, 65M12.

The article investigates the eigenvalue problem for ordinary onedimensional differential operator with nonlocal integral condition. Such a problem is met in the literature quite rarely and is considerably less investigated. Also the conditions for existence of non-positive eigenvalue or multiple eigenvalues are obtained.

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