M. Denche, "On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem", International Journal of Stochastic Analysis, vol. 12, Article ID 241293, 13 pages, 1999. https://doi.org/10.1155/S104895339900026X
On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem
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.
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