Electron. J. Diff. Equ., Vol. 2013 (2013), No. 242, pp. 1-12.

Existence and uniqueness for a two-point interface boundary value problem

Rakhim Aitbayev

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
email: aitbayev@nmt.edu

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