Differential and Integral Equations

Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces

Mustapha Cheggag, Angelo Favini, Rabah Labbas, Stéphane Maingot, and Ahmed Medeghri

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this paper we give some new results on Sturm-Liouville abstract problems of second-order differential equations of elliptic type in UMD spaces. Existence, uniqueness and maximal regularity of the strict solution are proved using the celebrated Dore-Venni theorem. This work completes the problems studied by Favini, Labbas, Maingot, Tanabe and Yagi under Dirichlet boundary conditions, see [6].

Article information

Differential Integral Equations, Volume 21, Number 9-10 (2008), 981-1000.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]
Secondary: 34B05: Linear boundary value problems 34G10: Linear equations [See also 47D06, 47D09] 35J25: Boundary value problems for second-order elliptic equations 35J40: Boundary value problems for higher-order elliptic equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations


Cheggag, Mustapha; Favini, Angelo; Labbas, Rabah; Maingot, Stéphane; Medeghri, Ahmed. Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces. Differential Integral Equations 21 (2008), no. 9-10, 981--1000. https://projecteuclid.org/euclid.die/1356038596

Export citation