Regular boundary value problems for ordinary differential-operator equations of higher order in umd banach spaces

We prove an isomorphism of nonlocal boundary value problems for higher order ordinary differential-operator equations generated by one operator in UMD Banach spaces in appropriate Sobolev and interpolation spaces. The main condition is given in terms of R-boundedness of some families of bounded operators generated by the resolvent of the operator of the equation. This implies maximal L _p-regularity for the problem. Then we study Fredholmnees of more general problems, namely, with linear abstract perturbation operators both in the equation and boundary conditions. We also present an application of obtained abstract results to boundary value problems for higher order elliptic partial differential equations.