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Apologies in advance if I'm being rather thick-headed...

If two simultaneous linear equations have no solution, it means that the equations are inconsistent and so graphically the two lines are parallel. But what does it mean when a boundary value problem has no solution? The cases of infinitely many solutions, and unique solution, are intuitively clear enough, but I'm having trouble coming to terms with the physical consequence of a BVP having no solution. Can someone help me put it in a physical framework? Is it possible for the given conditions of a BVP to be accurate (meaning the given system is not inconsistent), and yet for the BVP to have no solution?

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    No, I hadn't misinterpreted "inconsistent" at all. The inconsistency refers to the given system (its differential eqns together with the $b$oundary conditions), not to individual e$q$ns.2012-03-28

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