Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 3, Pages 279-291

On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem

M. Denche

Université de Constantine, Institut de Mathematiques, Constantine, Algeria

Received 1 July 1997; Revised 1 August 1998

Copyright © 1999 M. Denche. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the system of root functions. The results obtained are then applied to the study of a nonlocal parabolic transmission problem.