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
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.