## Differential and Integral Equations

### Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 21, Number 5-6 (2008), 497-512.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038630

Mathematical Reviews number (MathSciNet)
MR2483266

Zentralblatt MATH identifier
1224.34186

#### Citation

Favini, Angelo; Yakubov, Yakov. Higher order ordinary differential-operator equations on the whole axis in UMD Banach spaces. Differential Integral Equations 21 (2008), no. 5-6, 497--512. https://projecteuclid.org/euclid.die/1356038630