We use a direct approach for proving an isomorphism result for a general higher order abstract ordinary differential equation in a UMD Banach space. In fact, it gives maximal $L_p$-regularity property. As a consequence, we get some interpolation theorem (about intermediate derivatives). A situation of a higher order equation generated by one operator is also treated. Finally, we present some application to elliptic PDEs.
"Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces." Differential Integral Equations 21 (5-6) 497 - 512, 2008. https://doi.org/10.57262/die/1356038630