For linear ODE systems with arbitrary continuous boundary conditions in Sobolev spaces, the boundary-value operator is Fredholm with index rm-l, and kernel and cokernel dimensions equal those of an explicit characteristic matrix.
The solvability of inhomogeneous boundary-value prob- lems in Sobolev spaces
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Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions
For linear ODE systems with arbitrary continuous boundary conditions in Sobolev spaces, the boundary-value operator is Fredholm with index rm-l, and kernel and cokernel dimensions equal those of an explicit characteristic matrix.