Geodesic
Existence and uniqueness for a two-point interface boundary value problem
Electronic journal of differential equations, Tome 2013 (2013)
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.
Classification : 34B05, 34B10
Keywords: interface conditions, transmission conditions, two-point boundary value problem, discontinuous coefficients, existence and uniqueness 
@article{EJDE_2013__2013__a98,
     author = {Aitbayev,  Rakhim},
     title = {Existence and uniqueness for a two-point interface boundary value problem},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1292.34020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a98/}
}
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JO  - Electronic journal of differential equations
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%A Aitbayev,  Rakhim
%T Existence and uniqueness for a two-point interface boundary value problem
%J Electronic journal of differential equations
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%F EJDE_2013__2013__a98
Aitbayev,  Rakhim. Existence and uniqueness for a two-point interface boundary value problem. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a98/