We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundary-value problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem with typical interface such as perfect contact, non-perfect contact, and flux jump conditions.
Submitted August 23, 2013. Published October 31, 2013.
Math Subject Classifications: 34B05, 34B10.
Key Words: Interface conditions; transmission conditions; two-point boundary value problem; discontinuous coefficients; existence and uniqueness
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| Rakhim Aitbayev |
Department of Mathematics
New Mexico Institute of Mining and Technology
Socorro, New Mexico 87801, USA
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